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Simplifying 480 = -2x2 + 70x Reorder the terms: 480 = 70x + -2x2 Solving 480 = 70x + -2x2 Solving for variable 'x'. Reorder the terms: 480 + -70x + 2x2 = 70x + -70x + -2x2 + 2x2 Combine like terms: 70x + -70x = 0 480 + -70x + 2x2 = 0 + -2x2 + 2x2 480 + -70x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 480 + -70x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(240 + -35x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(240 + -35x + x2)' equal to zero and attempt to solve: Simplifying 240 + -35x + x2 = 0 Solving 240 + -35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-240' to each side of the equation. 240 + -35x + -240 + x2 = 0 + -240 Reorder the terms: 240 + -240 + -35x + x2 = 0 + -240 Combine like terms: 240 + -240 = 0 0 + -35x + x2 = 0 + -240 -35x + x2 = 0 + -240 Combine like terms: 0 + -240 = -240 -35x + x2 = -240 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = -240 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -240 + 306.25 Combine like terms: -240 + 306.25 = 66.25 306.25 + -35x + x2 = 66.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x + -17.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x + -17.5 = 8.139410298 Simplifying x + -17.5 = 8.139410298 Reorder the terms: -17.5 + x = 8.139410298 Solving -17.5 + x = 8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 8.139410298 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 8.139410298 + 17.5 x = 8.139410298 + 17.5 Combine like terms: 8.139410298 + 17.5 = 25.639410298 x = 25.639410298 Simplifying x = 25.639410298Subproblem 2
x + -17.5 = -8.139410298 Simplifying x + -17.5 = -8.139410298 Reorder the terms: -17.5 + x = -8.139410298 Solving -17.5 + x = -8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -8.139410298 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -8.139410298 + 17.5 x = -8.139410298 + 17.5 Combine like terms: -8.139410298 + 17.5 = 9.360589702 x = 9.360589702 Simplifying x = 9.360589702Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.639410298, 9.360589702}Solution
x = {25.639410298, 9.360589702}
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