4x(x+3)+2x=x-8

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Solution for 4x(x+3)+2x=x-8 equation:


Simplifying
4x(x + 3) + 2x = x + -8

Reorder the terms:
4x(3 + x) + 2x = x + -8
(3 * 4x + x * 4x) + 2x = x + -8
(12x + 4x2) + 2x = x + -8

Reorder the terms:
12x + 2x + 4x2 = x + -8

Combine like terms: 12x + 2x = 14x
14x + 4x2 = x + -8

Reorder the terms:
14x + 4x2 = -8 + x

Solving
14x + 4x2 = -8 + x

Solving for variable 'x'.

Reorder the terms:
8 + 14x + -1x + 4x2 = -8 + x + 8 + -1x

Combine like terms: 14x + -1x = 13x
8 + 13x + 4x2 = -8 + x + 8 + -1x

Reorder the terms:
8 + 13x + 4x2 = -8 + 8 + x + -1x

Combine like terms: -8 + 8 = 0
8 + 13x + 4x2 = 0 + x + -1x
8 + 13x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
8 + 13x + 4x2 = 0

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

Divide each side by '4'.
2 + 3.25x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 3.25x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 3.25x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3.25x + x2 = 0 + -2
3.25x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
3.25x + x2 = -2

The x term is 3.25x.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25x + 2.640625 + x2 = -2 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = -2 + 2.640625

Combine like terms: -2 + 2.640625 = 0.640625
2.640625 + 3.25x + x2 = 0.640625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(x + 1.625) equal to 0.80039053 and -0.80039053.

Subproblem 1

x + 1.625 = 0.80039053 Simplifying x + 1.625 = 0.80039053 Reorder the terms: 1.625 + x = 0.80039053 Solving 1.625 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 0.80039053 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 0.80039053 + -1.625 x = 0.80039053 + -1.625 Combine like terms: 0.80039053 + -1.625 = -0.82460947 x = -0.82460947 Simplifying x = -0.82460947

Subproblem 2

x + 1.625 = -0.80039053 Simplifying x + 1.625 = -0.80039053 Reorder the terms: 1.625 + x = -0.80039053 Solving 1.625 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -0.80039053 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -0.80039053 + -1.625 x = -0.80039053 + -1.625 Combine like terms: -0.80039053 + -1.625 = -2.42539053 x = -2.42539053 Simplifying x = -2.42539053

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.82460947, -2.42539053}

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