x(x+8)=72

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Solution for x(x+8)=72 equation:


Simplifying
x(x + 8) = 72

Reorder the terms:
x(8 + x) = 72
(8 * x + x * x) = 72
(8x + x2) = 72

Solving
8x + x2 = 72

Solving for variable 'x'.

Reorder the terms:
-72 + 8x + x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 8x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + 8x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 8x + x2 = 0 + 72
8x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
8x + x2 = 72

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 = 72 + 16

Reorder the terms:
16 + 8x + x2 = 72 + 16

Combine like terms: 72 + 16 = 88
16 + 8x + x2 = 88

Factor a perfect square on the left side:
(x + 4)(x + 4) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(x + 4) equal to 9.38083152 and -9.38083152.

Subproblem 1

x + 4 = 9.38083152 Simplifying x + 4 = 9.38083152 Reorder the terms: 4 + x = 9.38083152 Solving 4 + x = 9.38083152 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 = 9.38083152 + -4 Combine like terms: 4 + -4 = 0 0 + x = 9.38083152 + -4 x = 9.38083152 + -4 Combine like terms: 9.38083152 + -4 = 5.38083152 x = 5.38083152 Simplifying x = 5.38083152

Subproblem 2

x + 4 = -9.38083152 Simplifying x + 4 = -9.38083152 Reorder the terms: 4 + x = -9.38083152 Solving 4 + x = -9.38083152 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 = -9.38083152 + -4 Combine like terms: 4 + -4 = 0 0 + x = -9.38083152 + -4 x = -9.38083152 + -4 Combine like terms: -9.38083152 + -4 = -13.38083152 x = -13.38083152 Simplifying x = -13.38083152

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.38083152, -13.38083152}

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