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Simplifying 13x2 + 5x + -125 = -2x2 Reorder the terms: -125 + 5x + 13x2 = -2x2 Solving -125 + 5x + 13x2 = -2x2 Solving for variable 'x'. Combine like terms: 13x2 + 2x2 = 15x2 -125 + 5x + 15x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -125 + 5x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-25 + x + 3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-25 + x + 3x2)' equal to zero and attempt to solve: Simplifying -25 + x + 3x2 = 0 Solving -25 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.333333333 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + 0.3333333333x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + 0.3333333333x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + 0.3333333333x + x2 = 0 + 8.333333333 0.3333333333x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 0.3333333333x + x2 = 8.333333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 8.333333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 8.333333333 + 0.25 Combine like terms: 8.333333333 + 0.25 = 8.583333333 0.25 + 0.3333333333x + x2 = 8.583333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 8.583333333 Calculate the square root of the right side: 2.929732638 Break this problem into two subproblems by setting (x + 0.5) equal to 2.929732638 and -2.929732638.Subproblem 1
x + 0.5 = 2.929732638 Simplifying x + 0.5 = 2.929732638 Reorder the terms: 0.5 + x = 2.929732638 Solving 0.5 + x = 2.929732638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.929732638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.929732638 + -0.5 x = 2.929732638 + -0.5 Combine like terms: 2.929732638 + -0.5 = 2.429732638 x = 2.429732638 Simplifying x = 2.429732638Subproblem 2
x + 0.5 = -2.929732638 Simplifying x + 0.5 = -2.929732638 Reorder the terms: 0.5 + x = -2.929732638 Solving 0.5 + x = -2.929732638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.929732638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.929732638 + -0.5 x = -2.929732638 + -0.5 Combine like terms: -2.929732638 + -0.5 = -3.429732638 x = -3.429732638 Simplifying x = -3.429732638Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.429732638, -3.429732638}Solution
x = {2.429732638, -3.429732638}
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