(x+8)(x+8)=24

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Solution for (x+8)(x+8)=24 equation:


Simplifying
(x + 8)(x + 8) = 24

Reorder the terms:
(8 + x)(x + 8) = 24

Reorder the terms:
(8 + x)(8 + x) = 24

Multiply (8 + x) * (8 + x)
(8(8 + x) + x(8 + x)) = 24
((8 * 8 + x * 8) + x(8 + x)) = 24
((64 + 8x) + x(8 + x)) = 24
(64 + 8x + (8 * x + x * x)) = 24
(64 + 8x + (8x + x2)) = 24

Combine like terms: 8x + 8x = 16x
(64 + 16x + x2) = 24

Solving
64 + 16x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
64 + -24 + 16x + x2 = 24 + -24

Combine like terms: 64 + -24 = 40
40 + 16x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
40 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 16x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + 16x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 16x + x2 = 0 + -40
16x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
16x + x2 = -40

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -40 + 64

Reorder the terms:
64 + 16x + x2 = -40 + 64

Combine like terms: -40 + 64 = 24
64 + 16x + x2 = 24

Factor a perfect square on the left side:
(x + 8)(x + 8) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 8) equal to 4.898979486 and -4.898979486.

Subproblem 1

x + 8 = 4.898979486 Simplifying x + 8 = 4.898979486 Reorder the terms: 8 + x = 4.898979486 Solving 8 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 4.898979486 + -8 Combine like terms: 8 + -8 = 0 0 + x = 4.898979486 + -8 x = 4.898979486 + -8 Combine like terms: 4.898979486 + -8 = -3.101020514 x = -3.101020514 Simplifying x = -3.101020514

Subproblem 2

x + 8 = -4.898979486 Simplifying x + 8 = -4.898979486 Reorder the terms: 8 + x = -4.898979486 Solving 8 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -4.898979486 + -8 Combine like terms: 8 + -8 = 0 0 + x = -4.898979486 + -8 x = -4.898979486 + -8 Combine like terms: -4.898979486 + -8 = -12.898979486 x = -12.898979486 Simplifying x = -12.898979486

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.101020514, -12.898979486}

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