64x^2-92x-90=0

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Solution for 64x^2-92x-90=0 equation:


Simplifying
64x2 + -92x + -90 = 0

Reorder the terms:
-90 + -92x + 64x2 = 0

Solving
-90 + -92x + 64x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -46x + 32x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-45 + -46x + 32x2)' equal to zero and attempt to solve: Simplifying -45 + -46x + 32x2 = 0 Solving -45 + -46x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -1.40625 + -1.4375x + x2 = 0 Move the constant term to the right: Add '1.40625' to each side of the equation. -1.40625 + -1.4375x + 1.40625 + x2 = 0 + 1.40625 Reorder the terms: -1.40625 + 1.40625 + -1.4375x + x2 = 0 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + -1.4375x + x2 = 0 + 1.40625 -1.4375x + x2 = 0 + 1.40625 Combine like terms: 0 + 1.40625 = 1.40625 -1.4375x + x2 = 1.40625 The x term is -1.4375x. Take half its coefficient (-0.71875). Square it (0.5166015625) and add it to both sides. Add '0.5166015625' to each side of the equation. -1.4375x + 0.5166015625 + x2 = 1.40625 + 0.5166015625 Reorder the terms: 0.5166015625 + -1.4375x + x2 = 1.40625 + 0.5166015625 Combine like terms: 1.40625 + 0.5166015625 = 1.9228515625 0.5166015625 + -1.4375x + x2 = 1.9228515625 Factor a perfect square on the left side: (x + -0.71875)(x + -0.71875) = 1.9228515625 Calculate the square root of the right side: 1.386669233 Break this problem into two subproblems by setting (x + -0.71875) equal to 1.386669233 and -1.386669233.

Subproblem 1

x + -0.71875 = 1.386669233 Simplifying x + -0.71875 = 1.386669233 Reorder the terms: -0.71875 + x = 1.386669233 Solving -0.71875 + x = 1.386669233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.71875' to each side of the equation. -0.71875 + 0.71875 + x = 1.386669233 + 0.71875 Combine like terms: -0.71875 + 0.71875 = 0.00000 0.00000 + x = 1.386669233 + 0.71875 x = 1.386669233 + 0.71875 Combine like terms: 1.386669233 + 0.71875 = 2.105419233 x = 2.105419233 Simplifying x = 2.105419233

Subproblem 2

x + -0.71875 = -1.386669233 Simplifying x + -0.71875 = -1.386669233 Reorder the terms: -0.71875 + x = -1.386669233 Solving -0.71875 + x = -1.386669233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.71875' to each side of the equation. -0.71875 + 0.71875 + x = -1.386669233 + 0.71875 Combine like terms: -0.71875 + 0.71875 = 0.00000 0.00000 + x = -1.386669233 + 0.71875 x = -1.386669233 + 0.71875 Combine like terms: -1.386669233 + 0.71875 = -0.667919233 x = -0.667919233 Simplifying x = -0.667919233

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.105419233, -0.667919233}

Solution

x = {2.105419233, -0.667919233}

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