96=(5+x)x

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Solution for 96=(5+x)x equation:


Simplifying
96 = (5 + x) * x

Reorder the terms for easier multiplication:
96 = x(5 + x)
96 = (5 * x + x * x)
96 = (5x + x2)

Solving
96 = 5x + x2

Solving for variable 'x'.

Reorder the terms:
96 + -5x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
96 + -5x + -1x2 = 0 + x2 + -1x2
96 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
96 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-96 + 5x + x2 = 0

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + 5x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + 5x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + 5x + x2 = 0 + 96
5x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
5x + x2 = 96

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 96 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 96 + 6.25

Combine like terms: 96 + 6.25 = 102.25
6.25 + 5x + x2 = 102.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.111874208 and -10.111874208.

Subproblem 1

x + 2.5 = 10.111874208 Simplifying x + 2.5 = 10.111874208 Reorder the terms: 2.5 + x = 10.111874208 Solving 2.5 + x = 10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.111874208 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.111874208 + -2.5 x = 10.111874208 + -2.5 Combine like terms: 10.111874208 + -2.5 = 7.611874208 x = 7.611874208 Simplifying x = 7.611874208

Subproblem 2

x + 2.5 = -10.111874208 Simplifying x + 2.5 = -10.111874208 Reorder the terms: 2.5 + x = -10.111874208 Solving 2.5 + x = -10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.111874208 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.111874208 + -2.5 x = -10.111874208 + -2.5 Combine like terms: -10.111874208 + -2.5 = -12.611874208 x = -12.611874208 Simplifying x = -12.611874208

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.611874208, -12.611874208}

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