(10+x)x=128

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Solution for (10+x)x=128 equation:


Simplifying
(10 + x) * x = 128

Reorder the terms for easier multiplication:
x(10 + x) = 128
(10 * x + x * x) = 128
(10x + x2) = 128

Solving
10x + x2 = 128

Solving for variable 'x'.

Reorder the terms:
-128 + 10x + x2 = 128 + -128

Combine like terms: 128 + -128 = 0
-128 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '128' to each side of the equation.
-128 + 10x + 128 + x2 = 0 + 128

Reorder the terms:
-128 + 128 + 10x + x2 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + 10x + x2 = 0 + 128
10x + x2 = 0 + 128

Combine like terms: 0 + 128 = 128
10x + x2 = 128

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 128 + 25

Reorder the terms:
25 + 10x + x2 = 128 + 25

Combine like terms: 128 + 25 = 153
25 + 10x + x2 = 153

Factor a perfect square on the left side:
(x + 5)(x + 5) = 153

Calculate the square root of the right side: 12.369316877

Break this problem into two subproblems by setting 
(x + 5) equal to 12.369316877 and -12.369316877.

Subproblem 1

x + 5 = 12.369316877 Simplifying x + 5 = 12.369316877 Reorder the terms: 5 + x = 12.369316877 Solving 5 + x = 12.369316877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 12.369316877 + -5 Combine like terms: 5 + -5 = 0 0 + x = 12.369316877 + -5 x = 12.369316877 + -5 Combine like terms: 12.369316877 + -5 = 7.369316877 x = 7.369316877 Simplifying x = 7.369316877

Subproblem 2

x + 5 = -12.369316877 Simplifying x + 5 = -12.369316877 Reorder the terms: 5 + x = -12.369316877 Solving 5 + x = -12.369316877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -12.369316877 + -5 Combine like terms: 5 + -5 = 0 0 + x = -12.369316877 + -5 x = -12.369316877 + -5 Combine like terms: -12.369316877 + -5 = -17.369316877 x = -17.369316877 Simplifying x = -17.369316877

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.369316877, -17.369316877}

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