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Simplifying 8x2 + 60x + -64 = 0 Reorder the terms: -64 + 60x + 8x2 = 0 Solving -64 + 60x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-16 + 15x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-16 + 15x + 2x2)' equal to zero and attempt to solve: Simplifying -16 + 15x + 2x2 = 0 Solving -16 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + 7.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 7.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 7.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 7.5x + x2 = 0 + 8 7.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 7.5x + x2 = 8 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 8 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 8 + 14.0625 Combine like terms: 8 + 14.0625 = 22.0625 14.0625 + 7.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + 3.75) equal to 4.697073557 and -4.697073557.Subproblem 1
x + 3.75 = 4.697073557 Simplifying x + 3.75 = 4.697073557 Reorder the terms: 3.75 + x = 4.697073557 Solving 3.75 + x = 4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 4.697073557 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.697073557 + -3.75 x = 4.697073557 + -3.75 Combine like terms: 4.697073557 + -3.75 = 0.947073557 x = 0.947073557 Simplifying x = 0.947073557Subproblem 2
x + 3.75 = -4.697073557 Simplifying x + 3.75 = -4.697073557 Reorder the terms: 3.75 + x = -4.697073557 Solving 3.75 + x = -4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -4.697073557 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.697073557 + -3.75 x = -4.697073557 + -3.75 Combine like terms: -4.697073557 + -3.75 = -8.447073557 x = -8.447073557 Simplifying x = -8.447073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.947073557, -8.447073557}Solution
x = {0.947073557, -8.447073557}
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