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Simplifying -2x2 + -30x + 472 = 0 Reorder the terms: 472 + -30x + -2x2 = 0 Solving 472 + -30x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(236 + -15x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(236 + -15x + -1x2)' equal to zero and attempt to solve: Simplifying 236 + -15x + -1x2 = 0 Solving 236 + -15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -236 + 15x + x2 = 0 Move the constant term to the right: Add '236' to each side of the equation. -236 + 15x + 236 + x2 = 0 + 236 Reorder the terms: -236 + 236 + 15x + x2 = 0 + 236 Combine like terms: -236 + 236 = 0 0 + 15x + x2 = 0 + 236 15x + x2 = 0 + 236 Combine like terms: 0 + 236 = 236 15x + x2 = 236 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 = 236 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 236 + 56.25 Combine like terms: 236 + 56.25 = 292.25 56.25 + 15x + x2 = 292.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 292.25 Calculate the square root of the right side: 17.095320997 Break this problem into two subproblems by setting (x + 7.5) equal to 17.095320997 and -17.095320997.Subproblem 1
x + 7.5 = 17.095320997 Simplifying x + 7.5 = 17.095320997 Reorder the terms: 7.5 + x = 17.095320997 Solving 7.5 + x = 17.095320997 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 = 17.095320997 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 17.095320997 + -7.5 x = 17.095320997 + -7.5 Combine like terms: 17.095320997 + -7.5 = 9.595320997 x = 9.595320997 Simplifying x = 9.595320997Subproblem 2
x + 7.5 = -17.095320997 Simplifying x + 7.5 = -17.095320997 Reorder the terms: 7.5 + x = -17.095320997 Solving 7.5 + x = -17.095320997 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 = -17.095320997 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -17.095320997 + -7.5 x = -17.095320997 + -7.5 Combine like terms: -17.095320997 + -7.5 = -24.595320997 x = -24.595320997 Simplifying x = -24.595320997Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.595320997, -24.595320997}Solution
x = {9.595320997, -24.595320997}
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