2x(x+5)=x-8

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Solution for 2x(x+5)=x-8 equation:


Simplifying
2x(x + 5) = x + -8

Reorder the terms:
2x(5 + x) = x + -8
(5 * 2x + x * 2x) = x + -8
(10x + 2x2) = x + -8

Reorder the terms:
10x + 2x2 = -8 + x

Solving
10x + 2x2 = -8 + x

Solving for variable 'x'.

Reorder the terms:
8 + 10x + -1x + 2x2 = -8 + x + 8 + -1x

Combine like terms: 10x + -1x = 9x
8 + 9x + 2x2 = -8 + x + 8 + -1x

Reorder the terms:
8 + 9x + 2x2 = -8 + 8 + x + -1x

Combine like terms: -8 + 8 = 0
8 + 9x + 2x2 = 0 + x + -1x
8 + 9x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
8 + 9x + 2x2 = 0

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

Divide each side by '2'.
4 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 4.5x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 4.5x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 4.5x + x2 = 0 + -4
4.5x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
4.5x + x2 = -4

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -4 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -4 + 5.0625

Combine like terms: -4 + 5.0625 = 1.0625
5.0625 + 4.5x + x2 = 1.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(x + 2.25) equal to 1.030776406 and -1.030776406.

Subproblem 1

x + 2.25 = 1.030776406 Simplifying x + 2.25 = 1.030776406 Reorder the terms: 2.25 + x = 1.030776406 Solving 2.25 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 1.030776406 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 1.030776406 + -2.25 x = 1.030776406 + -2.25 Combine like terms: 1.030776406 + -2.25 = -1.219223594 x = -1.219223594 Simplifying x = -1.219223594

Subproblem 2

x + 2.25 = -1.030776406 Simplifying x + 2.25 = -1.030776406 Reorder the terms: 2.25 + x = -1.030776406 Solving 2.25 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -1.030776406 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -1.030776406 + -2.25 x = -1.030776406 + -2.25 Combine like terms: -1.030776406 + -2.25 = -3.280776406 x = -3.280776406 Simplifying x = -3.280776406

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.219223594, -3.280776406}

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