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Simplifying 4x2 + -134x = 570 Reorder the terms: -134x + 4x2 = 570 Solving -134x + 4x2 = 570 Solving for variable 'x'. Reorder the terms: -570 + -134x + 4x2 = 570 + -570 Combine like terms: 570 + -570 = 0 -570 + -134x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-285 + -67x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-285 + -67x + 2x2)' equal to zero and attempt to solve: Simplifying -285 + -67x + 2x2 = 0 Solving -285 + -67x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -142.5 + -33.5x + x2 = 0 Move the constant term to the right: Add '142.5' to each side of the equation. -142.5 + -33.5x + 142.5 + x2 = 0 + 142.5 Reorder the terms: -142.5 + 142.5 + -33.5x + x2 = 0 + 142.5 Combine like terms: -142.5 + 142.5 = 0.0 0.0 + -33.5x + x2 = 0 + 142.5 -33.5x + x2 = 0 + 142.5 Combine like terms: 0 + 142.5 = 142.5 -33.5x + x2 = 142.5 The x term is -33.5x. Take half its coefficient (-16.75). Square it (280.5625) and add it to both sides. Add '280.5625' to each side of the equation. -33.5x + 280.5625 + x2 = 142.5 + 280.5625 Reorder the terms: 280.5625 + -33.5x + x2 = 142.5 + 280.5625 Combine like terms: 142.5 + 280.5625 = 423.0625 280.5625 + -33.5x + x2 = 423.0625 Factor a perfect square on the left side: (x + -16.75)(x + -16.75) = 423.0625 Calculate the square root of the right side: 20.568483172 Break this problem into two subproblems by setting (x + -16.75) equal to 20.568483172 and -20.568483172.Subproblem 1
x + -16.75 = 20.568483172 Simplifying x + -16.75 = 20.568483172 Reorder the terms: -16.75 + x = 20.568483172 Solving -16.75 + x = 20.568483172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.75' to each side of the equation. -16.75 + 16.75 + x = 20.568483172 + 16.75 Combine like terms: -16.75 + 16.75 = 0.00 0.00 + x = 20.568483172 + 16.75 x = 20.568483172 + 16.75 Combine like terms: 20.568483172 + 16.75 = 37.318483172 x = 37.318483172 Simplifying x = 37.318483172Subproblem 2
x + -16.75 = -20.568483172 Simplifying x + -16.75 = -20.568483172 Reorder the terms: -16.75 + x = -20.568483172 Solving -16.75 + x = -20.568483172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.75' to each side of the equation. -16.75 + 16.75 + x = -20.568483172 + 16.75 Combine like terms: -16.75 + 16.75 = 0.00 0.00 + x = -20.568483172 + 16.75 x = -20.568483172 + 16.75 Combine like terms: -20.568483172 + 16.75 = -3.818483172 x = -3.818483172 Simplifying x = -3.818483172Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.318483172, -3.818483172}Solution
x = {37.318483172, -3.818483172}
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