8x^2+x-36=0

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Solution for 8x^2+x-36=0 equation:


Simplifying
8x2 + x + -36 = 0

Reorder the terms:
-36 + x + 8x2 = 0

Solving
-36 + x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-4.5 + 0.125x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 0.125x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 0.125x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 0.125x + x2 = 0 + 4.5
0.125x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
0.125x + x2 = 4.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.125x + 0.25 + x2 = 4.5 + 0.25

Reorder the terms:
0.25 + 0.125x + x2 = 4.5 + 0.25

Combine like terms: 4.5 + 0.25 = 4.75
0.25 + 0.125x + x2 = 4.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.179449472 and -2.179449472.

Subproblem 1

x + 0.5 = 2.179449472 Simplifying x + 0.5 = 2.179449472 Reorder the terms: 0.5 + x = 2.179449472 Solving 0.5 + x = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.179449472 + -0.5 x = 2.179449472 + -0.5 Combine like terms: 2.179449472 + -0.5 = 1.679449472 x = 1.679449472 Simplifying x = 1.679449472

Subproblem 2

x + 0.5 = -2.179449472 Simplifying x + 0.5 = -2.179449472 Reorder the terms: 0.5 + x = -2.179449472 Solving 0.5 + x = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.179449472 + -0.5 x = -2.179449472 + -0.5 Combine like terms: -2.179449472 + -0.5 = -2.679449472 x = -2.679449472 Simplifying x = -2.679449472

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.679449472, -2.679449472}

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