Question

Solve 2x^2 − 8x = −7

Answer 1

The answer to your question is below

Explanation:

2x² - 8x = - 7

Divide by 2

`(2)/(2) x^(2)  - (8)/(2) x    = (-7)/(2)`

Complete the trinomial

`x^(2)  - 4x + (2)^(2)  = (-7)/(2) + (2)^(2)`

Simplify

`x^(2)  - 4x  + (2)^(2)  = (- 7 + 4)/(2)`

`x^(2)  - 4x + 4 = (-3)/(2)`

Factor

(x - 2)² =
`(-3)/(2)`

Get the square root

`\sqrt{(x - 2)^(2)} = \sqrt{(-3)/(2)}`

Simplification

x - 2 =±
`\sqrt{(3)/(2)} i`

x₁ = 2 +
`\sqrt{(3)/(2)} i`

x₂ = 2 -
`\sqrt{(3)/(2)}`