Question

Solve 2x^2 − 8x = −7

Answer 1

Answer:

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Step-by-step explanation:

                                2x²  -   8x   =  - 7

Divide by 2

$\frac{2}{2} x^{2} - \frac{8}{2} x = \frac{-7}{2}$

Complete the trinomial

$x^{2} - 4x + (2)^{2} = \frac{-7}{2} + (2)^{2}$

Simplify

$x^{2} - 4x + (2)^{2} = \frac{- 7 + 4}{2}$

$x^{2} - 4x + 4 = \frac{-3}{2}$

Factor

(x - 2)²  =  $\frac{-3}{2}$

Get the square root

$\sqrt{(x - 2)^{2}} = \sqrt{\frac{-3}{2}}$

Simplification

               x - 2 =± $\sqrt{\frac{3}{2}} i$

      x₁ = 2 + $\sqrt{\frac{3}{2}} i$

       x₂ = 2 - $\sqrt{\frac{3}{2}}$