(x+16)(x)=72

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Solution for (x+16)(x)=72 equation:


Simplifying
(x + 16)(x) = 72

Reorder the terms:
(16 + x)(x) = 72

Reorder the terms for easier multiplication:
x(16 + x) = 72
(16 * x + x * x) = 72
(16x + x2) = 72

Solving
16x + x2 = 72

Solving for variable 'x'.

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

Combine like terms: 72 + -72 = 0
-72 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 16x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + 16x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 16x + x2 = 0 + 72
16x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
16x + x2 = 72

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 = 72 + 64

Reorder the terms:
64 + 16x + x2 = 72 + 64

Combine like terms: 72 + 64 = 136
64 + 16x + x2 = 136

Factor a perfect square on the left side:
(x + 8)(x + 8) = 136

Calculate the square root of the right side: 11.66190379

Break this problem into two subproblems by setting 
(x + 8) equal to 11.66190379 and -11.66190379.

Subproblem 1

x + 8 = 11.66190379 Simplifying x + 8 = 11.66190379 Reorder the terms: 8 + x = 11.66190379 Solving 8 + x = 11.66190379 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 = 11.66190379 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.66190379 + -8 x = 11.66190379 + -8 Combine like terms: 11.66190379 + -8 = 3.66190379 x = 3.66190379 Simplifying x = 3.66190379

Subproblem 2

x + 8 = -11.66190379 Simplifying x + 8 = -11.66190379 Reorder the terms: 8 + x = -11.66190379 Solving 8 + x = -11.66190379 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 = -11.66190379 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.66190379 + -8 x = -11.66190379 + -8 Combine like terms: -11.66190379 + -8 = -19.66190379 x = -19.66190379 Simplifying x = -19.66190379

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.66190379, -19.66190379}

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