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All Common Core: High School - Algebra Resources

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Flashcards: Solve Quadratic Equations by Inspection, Quadratic Formula, Factoring, Completing the Square, and Taking Square Roots: CCSS.Math.Content.HSA-REI.B.4b

Solve $- 11 x^{2} + 20 x - 44 = 0$

$x = \frac{21}{11} - \frac{8 i}{11} \sqrt{6} , x = - \frac{1}{11} + \frac{8 i}{11} \sqrt{6}$

$x = - \frac{12}{11} - \frac{8 i}{11} \sqrt{6} , x = \frac{230}{11} + \frac{8 i}{11} \sqrt{6}$

$x = \frac{20}{11} - \frac{16 i}{11} \sqrt{6} , x = - \frac{20}{11} - \frac{16 i}{11} \sqrt{6}$

$x = \frac{10}{11} - \frac{8 i}{11} \sqrt{6} , x = \frac{10}{11} + \frac{8 i}{11} \sqrt{6}$

$x = \frac{120}{11} - \frac{8 i}{11} \sqrt{6} , x = - \frac{100}{11} + \frac{8 i}{11} \sqrt{6}$

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Flashcards: Solve Quadratic Equations by Inspection, Quadratic Formula, Factoring, Completing the Square, and Taking Square Roots: CCSS.Math.Content.HSA-REI.B.4b

Solve $- 11 x^{2} + 20 x - 44 = 0$

Your answer:

$x = \frac{21}{11} - \frac{8 i}{11} \sqrt{6} , x = - \frac{1}{11} + \frac{8 i}{11} \sqrt{6}$

Your answer:

$x = - \frac{12}{11} - \frac{8 i}{11} \sqrt{6} , x = \frac{230}{11} + \frac{8 i}{11} \sqrt{6}$

Your answer:

$x = \frac{20}{11} - \frac{16 i}{11} \sqrt{6} , x = - \frac{20}{11} - \frac{16 i}{11} \sqrt{6}$

Your answer:

$x = \frac{120}{11} - \frac{8 i}{11} \sqrt{6} , x = - \frac{100}{11} + \frac{8 i}{11} \sqrt{6}$

Correct answer:

$x = \frac{10}{11} - \frac{8 i}{11} \sqrt{6} , x = \frac{10}{11} + \frac{8 i}{11} \sqrt{6}$

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

$\frac{ -b \pm\sqrt{ b^{2} - 4 a c}}{2a}$

$\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ correspond to coefficients in the quadratic equation, which is

$a x^{2} + b x - 44 = 0$

In this case , , and .

$\frac{ -20 \pm\sqrt{ 20 ^2- 4 \cdot -11 \cdot -44 }}{ 2 \cdot -11 }$

$\frac{ -20 \pm\sqrt{ 400 - 1936 }}{ -22 }$

$\frac{ -20 \pm\sqrt{ -1536 }}{ -22 }$

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an $\uptext{i}$ , outside the square root sign, and then do normal operations.

$\frac{ -20 \pm i \sqrt{ 1536 }}{ -22 }$

Now we split this up into two equations.

$\frac{ -20 + i \sqrt{ 1536 }}{ -22 }$

$\frac{10}{11} + \frac{8 i}{11} \sqrt{6}$

$\frac{ -20 - i \sqrt{ 1536 }}{ -22 }$

$\frac{10}{11} - \frac{8 i}{11} \sqrt{6}$

So our solutions are $x = \frac{10}{11} - \frac{8 i}{11} \sqrt{6}$ and $x = \frac{10}{11} + \frac{8 i}{11} \sqrt{6}$

Flashcards: Solve Quadratic Equations by Inspection, Quadratic Formula, Factoring, Completing the Square, and Taking Square Roots: CCSS.Math.Content.HSA-REI.B.4b

Solve $18 x^{2} - 14 x + 41 = 0$

$x = \frac{7}{18} - \frac{\sqrt{689} i}{18} , x = \frac{7}{18} + \frac{\sqrt{689} i}{18}$

$x = \frac{187}{18} - \frac{\sqrt{689} i}{18} , x = - \frac{173}{18} + \frac{\sqrt{689} i}{18}$

$x = \frac{25}{18} - \frac{\sqrt{689} i}{18} , x = - \frac{11}{18} + \frac{\sqrt{689} i}{18}$

$x = - \frac{29}{18} - \frac{\sqrt{689} i}{18} , x = \frac{367}{18} + \frac{\sqrt{689} i}{18}$

$x = \frac{7}{9} - \frac{\sqrt{689} i}{9} , x = - \frac{7}{9} - \frac{\sqrt{689} i}{9}$

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Flashcards: Solve Quadratic Equations by Inspection, Quadratic Formula, Factoring, Completing the Square, and Taking Square Roots: CCSS.Math.Content.HSA-REI.B.4b

Solve $18 x^{2} - 14 x + 41 = 0$

Your answer:

$x = \frac{187}{18} - \frac{\sqrt{689} i}{18} , x = - \frac{173}{18} + \frac{\sqrt{689} i}{18}$

Your answer:

$x = \frac{25}{18} - \frac{\sqrt{689} i}{18} , x = - \frac{11}{18} + \frac{\sqrt{689} i}{18}$

Your answer:

$x = - \frac{29}{18} - \frac{\sqrt{689} i}{18} , x = \frac{367}{18} + \frac{\sqrt{689} i}{18}$

Your answer:

$x = \frac{7}{9} - \frac{\sqrt{689} i}{9} , x = - \frac{7}{9} - \frac{\sqrt{689} i}{9}$

Correct answer:

$x = \frac{7}{18} - \frac{\sqrt{689} i}{18} , x = \frac{7}{18} + \frac{\sqrt{689} i}{18}$

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

$\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$

$\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ correspond to coefficients in the quadratic equation, which is

$a x^{2} + b x + 41 = 0$

In this case , , and .

$\frac{ 14 \pm\sqrt{ -14 ^2- 4 \cdot 18 \cdot 41 }}{ 2 \cdot 18 }$

$\frac{ 14 \pm\sqrt{ 196 - 2952 }}{ 36 }$

$\frac{ 14 \pm\sqrt{ -2756 }}{ 36 }$

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an $\uptext{i}$ , outside the square root sign, and then do normal operations.

$\frac{ 14 \pm i \sqrt{ 2756 }}{ 36 }$

Now we split this up into two equations.

$\frac{ 14 + i \sqrt{ 2756 }}{ 36 }$

$\frac{7}{18} + \frac{\sqrt{689} i}{18}$

$\frac{ 14 - i \sqrt{ 2756 }}{ 36 }$

$\frac{7}{18} - \frac{\sqrt{689} i}{18}$

So our solutions are $x = \frac{7}{18} - \frac{\sqrt{689} i}{18}$ and $x = \frac{7}{18} + \frac{\sqrt{689} i}{18}$

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All Common Core: High School - Algebra Resources

Flashcards: Solve Quadratic Equations by Inspection, Quadratic Formula, Factoring, Completing the Square, and Taking Square Roots: CCSS.Math.Content.HSA-REI.B.4b

Flashcards: Solve Quadratic Equations by Inspection, Quadratic Formula, Factoring, Completing the Square, and Taking Square Roots: CCSS.Math.Content.HSA-REI.B.4b

Flashcards: Solve Quadratic Equations by Inspection, Quadratic Formula, Factoring, Completing the Square, and Taking Square Roots: CCSS.Math.Content.HSA-REI.B.4b

Flashcards: Solve Quadratic Equations by Inspection, Quadratic Formula, Factoring, Completing the Square, and Taking Square Roots: CCSS.Math.Content.HSA-REI.B.4b

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