8x^2+27x-8=0

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


Simplifying
8x2 + 27x + -8 = 0

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

Solving
-8 + 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'.
-1 + 3.375x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 3.375x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 3.375x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3.375x + x2 = 0 + 1
3.375x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
3.375x + x2 = 1

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 = 1 + 2.84765625

Reorder the terms:
2.84765625 + 3.375x + x2 = 1 + 2.84765625

Combine like terms: 1 + 2.84765625 = 3.84765625
2.84765625 + 3.375x + x2 = 3.84765625

Factor a perfect square on the left side:
(x + 1.6875)(x + 1.6875) = 3.84765625

Calculate the square root of the right side: 1.961544353

Break this problem into two subproblems by setting 
(x + 1.6875) equal to 1.961544353 and -1.961544353.

Subproblem 1

x + 1.6875 = 1.961544353 Simplifying x + 1.6875 = 1.961544353 Reorder the terms: 1.6875 + x = 1.961544353 Solving 1.6875 + x = 1.961544353 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 = 1.961544353 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = 1.961544353 + -1.6875 x = 1.961544353 + -1.6875 Combine like terms: 1.961544353 + -1.6875 = 0.274044353 x = 0.274044353 Simplifying x = 0.274044353

Subproblem 2

x + 1.6875 = -1.961544353 Simplifying x + 1.6875 = -1.961544353 Reorder the terms: 1.6875 + x = -1.961544353 Solving 1.6875 + x = -1.961544353 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 = -1.961544353 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = -1.961544353 + -1.6875 x = -1.961544353 + -1.6875 Combine like terms: -1.961544353 + -1.6875 = -3.649044353 x = -3.649044353 Simplifying x = -3.649044353

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.274044353, -3.649044353}

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