x^2+8x=32

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Solution for x^2+8x=32 equation:


Simplifying
x2 + 8x = 32

Reorder the terms:
8x + x2 = 32

Solving
8x + x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + 8x + x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 8x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 8x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 8x + x2 = 0 + 32
8x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
8x + x2 = 32

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 32 + 16

Reorder the terms:
16 + 8x + x2 = 32 + 16

Combine like terms: 32 + 16 = 48
16 + 8x + x2 = 48

Factor a perfect square on the left side:
(x + 4)(x + 4) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(x + 4) equal to 6.92820323 and -6.92820323.

Subproblem 1

x + 4 = 6.92820323 Simplifying x + 4 = 6.92820323 Reorder the terms: 4 + x = 6.92820323 Solving 4 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 6.92820323 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.92820323 + -4 x = 6.92820323 + -4 Combine like terms: 6.92820323 + -4 = 2.92820323 x = 2.92820323 Simplifying x = 2.92820323

Subproblem 2

x + 4 = -6.92820323 Simplifying x + 4 = -6.92820323 Reorder the terms: 4 + x = -6.92820323 Solving 4 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -6.92820323 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.92820323 + -4 x = -6.92820323 + -4 Combine like terms: -6.92820323 + -4 = -10.92820323 x = -10.92820323 Simplifying x = -10.92820323

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.92820323, -10.92820323}

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