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Solve the following equation using the quadratic formula.

x^2 - 8x + 97 = 0
А.x = 8 + 18i and x = 8 – 18i
B.x= 8 + 18i and x = 8 - 18i
C.x= 4 + 9i and x = 4 - 9i
D. x= 4 + 9i and x= -4 - 9i

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wegnerkolmp2741o

Answer:

x = 4   ±9i

Step-by-step explanation:

x^2 - 8x + 97 = 0

Complete the square by subtracting 97 from each side

x^2 - 8x =- 97

Take the coefficient of x

-8 and divide by 2

-8/2 = -4

Then square it

(-4)^2 = 16

Add it to each side

x^2 - 8x + 16 = -97+16

(x-4)^2 = -81

Take the square root of each side

x-4 = ±sqrt(-81)

x-4 = ±9i

Add 4 to each side

x = 4   ±9i

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Answer:

C. x= 4 + 9i or x = 4 - 9i

Step-by-step explanation:

[tex]x^2 - 8x + 97 = 0[/tex]

Use the quadratic formula.

[tex]\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Substitute a = 1, b = -8, and c = 97.

[tex]\frac{-\left(-8\right)\pm\sqrt{\left(-8\right)^2-4\times 1\times 97}}{2\times 1}[/tex]

Evaluate.

[tex]\frac{8\pm\sqrt{324}i}{2\times 1}[/tex]

[tex]\frac{8\pm18i}{2}[/tex]

[tex]4\pm9i[/tex]

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