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What are the solutions of the quadratic equation x^2 - 10x = -34?

A. x = -8, -2
B. x = 5 + - 3i
C. x = -5 + - 3i
D. x = - 5 + -√59

User Mhlavacka
by
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1 Answer

1 vote

Final answer:

The solutions of the quadratic equation x^2 - 10x = -34 are x = 5 + 3i and x = 5 - 3i, which correspond to option B, when using the quadratic formula with complex numbers.

Step-by-step explanation:

We need to solve the quadratic equation x^2 - 10x = -34 by first bringing it to standard form, which means everything on one side of the equation set equal to zero. Thus, we add 34 to both sides:

x^2 - 10x + 34 = 0

To solve this quadratic equation, we use the quadratic formula:

x = ∛(-b ± √(b^2 - 4ac))/(2a)

Where a, b, and c are coefficients from the quadratic equation ax^2 + bx + c = 0. For our equation, a is 1, b is -10, and c is 34.

Substituting these values into the quadratic formula, we get:

x = (-(-10) ± √((-10)^2 - 4(1)(34)))/(2(1))

x = (10 ± √(100 - 136))/(2)

Since 100 - 136 is negative, we will have complex numbers as solutions:

x = (10 ± √(-36))/(2)

x = 5 ± 3i

Thus, the solutions to the equation are x = 5 + 3i and x = 5 - 3i, which corresponds to option B.

User Astupidname
by
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