x=8x^2+12x-20

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Solution for x=8x^2+12x-20 equation:


Simplifying
x = 8x2 + 12x + -20

Reorder the terms:
x = -20 + 12x + 8x2

Solving
x = -20 + 12x + 8x2

Solving for variable 'x'.

Reorder the terms:
20 + x + -12x + -8x2 = -20 + 12x + 8x2 + 20 + -12x + -8x2

Combine like terms: x + -12x = -11x
20 + -11x + -8x2 = -20 + 12x + 8x2 + 20 + -12x + -8x2

Reorder the terms:
20 + -11x + -8x2 = -20 + 20 + 12x + -12x + 8x2 + -8x2

Combine like terms: -20 + 20 = 0
20 + -11x + -8x2 = 0 + 12x + -12x + 8x2 + -8x2
20 + -11x + -8x2 = 12x + -12x + 8x2 + -8x2

Combine like terms: 12x + -12x = 0
20 + -11x + -8x2 = 0 + 8x2 + -8x2
20 + -11x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
20 + -11x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-2.5 + 1.375x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 1.375x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 1.375x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 1.375x + x2 = 0 + 2.5
1.375x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
1.375x + x2 = 2.5

The x term is 1.375x.  Take half its coefficient (0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
1.375x + 0.47265625 + x2 = 2.5 + 0.47265625

Reorder the terms:
0.47265625 + 1.375x + x2 = 2.5 + 0.47265625

Combine like terms: 2.5 + 0.47265625 = 2.97265625
0.47265625 + 1.375x + x2 = 2.97265625

Factor a perfect square on the left side:
(x + 0.6875)(x + 0.6875) = 2.97265625

Calculate the square root of the right side: 1.724139278

Break this problem into two subproblems by setting 
(x + 0.6875) equal to 1.724139278 and -1.724139278.

Subproblem 1

x + 0.6875 = 1.724139278 Simplifying x + 0.6875 = 1.724139278 Reorder the terms: 0.6875 + x = 1.724139278 Solving 0.6875 + x = 1.724139278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = 1.724139278 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 1.724139278 + -0.6875 x = 1.724139278 + -0.6875 Combine like terms: 1.724139278 + -0.6875 = 1.036639278 x = 1.036639278 Simplifying x = 1.036639278

Subproblem 2

x + 0.6875 = -1.724139278 Simplifying x + 0.6875 = -1.724139278 Reorder the terms: 0.6875 + x = -1.724139278 Solving 0.6875 + x = -1.724139278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = -1.724139278 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -1.724139278 + -0.6875 x = -1.724139278 + -0.6875 Combine like terms: -1.724139278 + -0.6875 = -2.411639278 x = -2.411639278 Simplifying x = -2.411639278

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.036639278, -2.411639278}

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