Question

Solve the following equations:
5x-(x+2)^2=x^2-8+x

Answer 1

x = √2 = 1.414

Explanation:

5x-(x+2)^2=x^2-8+x

since (x+2)^2 = x^2 + 2(x)(2) + 2^2 = x^2 + 4x + 4

so

5x - (x^2 + 4x + 4) = x^2 + x - 8

-x^2 + x - 4 = x^2 + x - 8

x^2 + x^2 + x - x = -4 + 8

2x^2 = 4

x^2 = 2

x = √2 = 1.414

Answer 2

`x = √(2) = 1.414 \\ x = - √(2) = - 1.414`

Explanation:

`5x - {(x + 2)}^(2) = {x}^(2) - 8 + x \\ \\ 5x - ( {x}^(2) + 4x + 4) = {x}^(2) - 8 + x \\ \\ 5x - {x}^(2) - 4x - 4 = {x}^(2) - 8 + x \\ \\ - {x}^(2) + x - 4 = {x}^(2) - 8 + x \\ \\ {x}^(2) + {x}^(2) + x - x = 8 - 4 \\ \\ 2 {x}^(2) = 4 \\ \\ {x}^(2) = (4)/(2) \\ \\ {x}^(2) = 2 \\ \\ x = √(2) = 1.414 \\ x = - √(2) = - 1.414`