144=(5+x)x

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Solution for 144=(5+x)x equation:


Simplifying
144 = (5 + x) * x

Reorder the terms for easier multiplication:
144 = x(5 + x)
144 = (5 * x + x * x)
144 = (5x + x2)

Solving
144 = 5x + x2

Solving for variable 'x'.

Reorder the terms:
144 + -5x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
144 + -5x + -1x2 = 0 + x2 + -1x2
144 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
144 + -5x + -1x2 = 0

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

Divide each side by '-1'.
-144 + 5x + x2 = 0

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 5x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + 5x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 5x + x2 = 0 + 144
5x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
5x + x2 = 144

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 = 144 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 144 + 6.25

Combine like terms: 144 + 6.25 = 150.25
6.25 + 5x + x2 = 150.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 150.25

Calculate the square root of the right side: 12.257650672

Break this problem into two subproblems by setting 
(x + 2.5) equal to 12.257650672 and -12.257650672.

Subproblem 1

x + 2.5 = 12.257650672 Simplifying x + 2.5 = 12.257650672 Reorder the terms: 2.5 + x = 12.257650672 Solving 2.5 + x = 12.257650672 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 = 12.257650672 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 12.257650672 + -2.5 x = 12.257650672 + -2.5 Combine like terms: 12.257650672 + -2.5 = 9.757650672 x = 9.757650672 Simplifying x = 9.757650672

Subproblem 2

x + 2.5 = -12.257650672 Simplifying x + 2.5 = -12.257650672 Reorder the terms: 2.5 + x = -12.257650672 Solving 2.5 + x = -12.257650672 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 = -12.257650672 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -12.257650672 + -2.5 x = -12.257650672 + -2.5 Combine like terms: -12.257650672 + -2.5 = -14.757650672 x = -14.757650672 Simplifying x = -14.757650672

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.757650672, -14.757650672}

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