Answer:
The answer to your question is below
Step-by-step explanation:
2x² - 8x = - 7
Divide by 2
[tex]\frac{2}{2} x^{2} - \frac{8}{2} x = \frac{-7}{2}[/tex]
Complete the trinomial
[tex]x^{2} - 4x + (2)^{2} = \frac{-7}{2} + (2)^{2}[/tex]
Simplify
[tex]x^{2} - 4x + (2)^{2} = \frac{- 7 + 4}{2}[/tex]
[tex]x^{2} - 4x + 4 = \frac{-3}{2}[/tex]
Factor
(x - 2)² = [tex]\frac{-3}{2}[/tex]
Get the square root
[tex]\sqrt{(x - 2)^{2}} = \sqrt{\frac{-3}{2}}[/tex]
Simplification
x - 2 =± [tex]\sqrt{\frac{3}{2}} i[/tex]
x₁ = 2 + [tex]\sqrt{\frac{3}{2}} i[/tex]
x₂ = 2 - [tex]\sqrt{\frac{3}{2}}[/tex]
