Question

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

Answer 1

Answer:

$x = \sqrt{2} = 1.414 \\ x = - \sqrt{2} = - 1.414$

Step-by-step explanation:

$5x - {(x + 2)}^{2} = {x}^{2} - 8 + x \\ \\ 5x - ( {x}^{2} + 4x + 4) = {x}^{2} - 8 + x \\ \\ 5x - {x}^{2} - 4x - 4 = {x}^{2} - 8 + x \\ \\ - {x}^{2} + x - 4 = {x}^{2} - 8 + x \\ \\ {x}^{2} + {x}^{2} + x - x = 8 - 4 \\ \\ 2 {x}^{2} = 4 \\ \\ {x}^{2} = \frac{4}{2} \\ \\ {x}^{2} = 2 \\ \\ x = \sqrt{2} = 1.414 \\ x = - \sqrt{2} = - 1.414$

Answer 2

Answer:

x = √2 = 1.414

Step-by-step 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