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Simplifying 4x2 + 60x + -166 = 0 Reorder the terms: -166 + 60x + 4x2 = 0 Solving -166 + 60x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-83 + 30x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-83 + 30x + 2x2)' equal to zero and attempt to solve: Simplifying -83 + 30x + 2x2 = 0 Solving -83 + 30x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -41.5 + 15x + x2 = 0 Move the constant term to the right: Add '41.5' to each side of the equation. -41.5 + 15x + 41.5 + x2 = 0 + 41.5 Reorder the terms: -41.5 + 41.5 + 15x + x2 = 0 + 41.5 Combine like terms: -41.5 + 41.5 = 0.0 0.0 + 15x + x2 = 0 + 41.5 15x + x2 = 0 + 41.5 Combine like terms: 0 + 41.5 = 41.5 15x + x2 = 41.5 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 41.5 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 41.5 + 56.25 Combine like terms: 41.5 + 56.25 = 97.75 56.25 + 15x + x2 = 97.75 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 97.75 Calculate the square root of the right side: 9.886859967 Break this problem into two subproblems by setting (x + 7.5) equal to 9.886859967 and -9.886859967.Subproblem 1
x + 7.5 = 9.886859967 Simplifying x + 7.5 = 9.886859967 Reorder the terms: 7.5 + x = 9.886859967 Solving 7.5 + x = 9.886859967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 9.886859967 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.886859967 + -7.5 x = 9.886859967 + -7.5 Combine like terms: 9.886859967 + -7.5 = 2.386859967 x = 2.386859967 Simplifying x = 2.386859967Subproblem 2
x + 7.5 = -9.886859967 Simplifying x + 7.5 = -9.886859967 Reorder the terms: 7.5 + x = -9.886859967 Solving 7.5 + x = -9.886859967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -9.886859967 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.886859967 + -7.5 x = -9.886859967 + -7.5 Combine like terms: -9.886859967 + -7.5 = -17.386859967 x = -17.386859967 Simplifying x = -17.386859967Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.386859967, -17.386859967}Solution
x = {2.386859967, -17.386859967}
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