8x^2+27x-58.5=0

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Solution for 8x^2+27x-58.5=0 equation:


Simplifying
8x2 + 27x + -58.5 = 0

Reorder the terms:
-58.5 + 27x + 8x2 = 0

Solving
-58.5 + 27x + 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'.
-7.3125 + 3.375x + x2 = 0

Move the constant term to the right:

Add '7.3125' to each side of the equation.
-7.3125 + 3.375x + 7.3125 + x2 = 0 + 7.3125

Reorder the terms:
-7.3125 + 7.3125 + 3.375x + x2 = 0 + 7.3125

Combine like terms: -7.3125 + 7.3125 = 0.0000
0.0000 + 3.375x + x2 = 0 + 7.3125
3.375x + x2 = 0 + 7.3125

Combine like terms: 0 + 7.3125 = 7.3125
3.375x + x2 = 7.3125

The x term is 3.375x.  Take half its coefficient (1.6875).
Square it (2.84765625) and add it to both sides.

Add '2.84765625' to each side of the equation.
3.375x + 2.84765625 + x2 = 7.3125 + 2.84765625

Reorder the terms:
2.84765625 + 3.375x + x2 = 7.3125 + 2.84765625

Combine like terms: 7.3125 + 2.84765625 = 10.16015625
2.84765625 + 3.375x + x2 = 10.16015625

Factor a perfect square on the left side:
(x + 1.6875)(x + 1.6875) = 10.16015625

Calculate the square root of the right side: 3.1875

Break this problem into two subproblems by setting 
(x + 1.6875) equal to 3.1875 and -3.1875.

Subproblem 1

x + 1.6875 = 3.1875 Simplifying x + 1.6875 = 3.1875 Reorder the terms: 1.6875 + x = 3.1875 Solving 1.6875 + x = 3.1875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6875' to each side of the equation. 1.6875 + -1.6875 + x = 3.1875 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = 3.1875 + -1.6875 x = 3.1875 + -1.6875 Combine like terms: 3.1875 + -1.6875 = 1.5 x = 1.5 Simplifying x = 1.5

Subproblem 2

x + 1.6875 = -3.1875 Simplifying x + 1.6875 = -3.1875 Reorder the terms: 1.6875 + x = -3.1875 Solving 1.6875 + x = -3.1875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6875' to each side of the equation. 1.6875 + -1.6875 + x = -3.1875 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = -3.1875 + -1.6875 x = -3.1875 + -1.6875 Combine like terms: -3.1875 + -1.6875 = -4.875 x = -4.875 Simplifying x = -4.875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.5, -4.875}

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