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Simplifying 8x2 + 58x + -120 = 0 Reorder the terms: -120 + 58x + 8x2 = 0 Solving -120 + 58x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + 29x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + 29x + 4x2)' equal to zero and attempt to solve: Simplifying -60 + 29x + 4x2 = 0 Solving -60 + 29x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15 + 7.25x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 7.25x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 7.25x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 7.25x + x2 = 0 + 15 7.25x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 7.25x + x2 = 15 The x term is 7.25x. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25x + 13.140625 + x2 = 15 + 13.140625 Reorder the terms: 13.140625 + 7.25x + x2 = 15 + 13.140625 Combine like terms: 15 + 13.140625 = 28.140625 13.140625 + 7.25x + x2 = 28.140625 Factor a perfect square on the left side: (x + 3.625)(x + 3.625) = 28.140625 Calculate the square root of the right side: 5.304773793 Break this problem into two subproblems by setting (x + 3.625) equal to 5.304773793 and -5.304773793.Subproblem 1
x + 3.625 = 5.304773793 Simplifying x + 3.625 = 5.304773793 Reorder the terms: 3.625 + x = 5.304773793 Solving 3.625 + x = 5.304773793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = 5.304773793 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = 5.304773793 + -3.625 x = 5.304773793 + -3.625 Combine like terms: 5.304773793 + -3.625 = 1.679773793 x = 1.679773793 Simplifying x = 1.679773793Subproblem 2
x + 3.625 = -5.304773793 Simplifying x + 3.625 = -5.304773793 Reorder the terms: 3.625 + x = -5.304773793 Solving 3.625 + x = -5.304773793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = -5.304773793 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = -5.304773793 + -3.625 x = -5.304773793 + -3.625 Combine like terms: -5.304773793 + -3.625 = -8.929773793 x = -8.929773793 Simplifying x = -8.929773793Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.679773793, -8.929773793}Solution
x = {1.679773793, -8.929773793}
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