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Simplifying 2x2 + -368x + -33560 = 0 Reorder the terms: -33560 + -368x + 2x2 = 0 Solving -33560 + -368x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-16780 + -184x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16780 + -184x + x2)' equal to zero and attempt to solve: Simplifying -16780 + -184x + x2 = 0 Solving -16780 + -184x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16780' to each side of the equation. -16780 + -184x + 16780 + x2 = 0 + 16780 Reorder the terms: -16780 + 16780 + -184x + x2 = 0 + 16780 Combine like terms: -16780 + 16780 = 0 0 + -184x + x2 = 0 + 16780 -184x + x2 = 0 + 16780 Combine like terms: 0 + 16780 = 16780 -184x + x2 = 16780 The x term is -184x. Take half its coefficient (-92). Square it (8464) and add it to both sides. Add '8464' to each side of the equation. -184x + 8464 + x2 = 16780 + 8464 Reorder the terms: 8464 + -184x + x2 = 16780 + 8464 Combine like terms: 16780 + 8464 = 25244 8464 + -184x + x2 = 25244 Factor a perfect square on the left side: (x + -92)(x + -92) = 25244 Calculate the square root of the right side: 158.883605196 Break this problem into two subproblems by setting (x + -92) equal to 158.883605196 and -158.883605196.Subproblem 1
x + -92 = 158.883605196 Simplifying x + -92 = 158.883605196 Reorder the terms: -92 + x = 158.883605196 Solving -92 + x = 158.883605196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '92' to each side of the equation. -92 + 92 + x = 158.883605196 + 92 Combine like terms: -92 + 92 = 0 0 + x = 158.883605196 + 92 x = 158.883605196 + 92 Combine like terms: 158.883605196 + 92 = 250.883605196 x = 250.883605196 Simplifying x = 250.883605196Subproblem 2
x + -92 = -158.883605196 Simplifying x + -92 = -158.883605196 Reorder the terms: -92 + x = -158.883605196 Solving -92 + x = -158.883605196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '92' to each side of the equation. -92 + 92 + x = -158.883605196 + 92 Combine like terms: -92 + 92 = 0 0 + x = -158.883605196 + 92 x = -158.883605196 + 92 Combine like terms: -158.883605196 + 92 = -66.883605196 x = -66.883605196 Simplifying x = -66.883605196Solution
The solution to the problem is based on the solutions from the subproblems. x = {250.883605196, -66.883605196}Solution
x = {250.883605196, -66.883605196}
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