x^2+(x+8)=40

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Solution for x^2+(x+8)=40 equation:


Simplifying
x2 + (x + 8) = 40

Reorder the terms:
x2 + (8 + x) = 40

Remove parenthesis around (8 + x)
x2 + 8 + x = 40

Reorder the terms:
8 + x + x2 = 40

Solving
8 + x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
8 + -40 + x + x2 = 40 + -40

Combine like terms: 8 + -40 = -32
-32 + x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-32 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + x + x2 = 0 + 32
x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
x + x2 = 32

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 32 + 0.25

Reorder the terms:
0.25 + x + x2 = 32 + 0.25

Combine like terms: 32 + 0.25 = 32.25
0.25 + x + x2 = 32.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.678908346 and -5.678908346.

Subproblem 1

x + 0.5 = 5.678908346 Simplifying x + 0.5 = 5.678908346 Reorder the terms: 0.5 + x = 5.678908346 Solving 0.5 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.678908346 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.678908346 + -0.5 x = 5.678908346 + -0.5 Combine like terms: 5.678908346 + -0.5 = 5.178908346 x = 5.178908346 Simplifying x = 5.178908346

Subproblem 2

x + 0.5 = -5.678908346 Simplifying x + 0.5 = -5.678908346 Reorder the terms: 0.5 + x = -5.678908346 Solving 0.5 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.678908346 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.678908346 + -0.5 x = -5.678908346 + -0.5 Combine like terms: -5.678908346 + -0.5 = -6.178908346 x = -6.178908346 Simplifying x = -6.178908346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.178908346, -6.178908346}

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