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Simplifying -1.624x2 + 38.653x + -178.768 = 0 Reorder the terms: -178.768 + 38.653x + -1.624x2 = 0 Solving -178.768 + 38.653x + -1.624x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.624 the coefficient of the squared term: Divide each side by '-1.624'. 110.0788177 + -23.80110837x + x2 = 0 Move the constant term to the right: Add '-110.0788177' to each side of the equation. 110.0788177 + -23.80110837x + -110.0788177 + x2 = 0 + -110.0788177 Reorder the terms: 110.0788177 + -110.0788177 + -23.80110837x + x2 = 0 + -110.0788177 Combine like terms: 110.0788177 + -110.0788177 = 0.0000000 0.0000000 + -23.80110837x + x2 = 0 + -110.0788177 -23.80110837x + x2 = 0 + -110.0788177 Combine like terms: 0 + -110.0788177 = -110.0788177 -23.80110837x + x2 = -110.0788177 The x term is -23.80110837x. Take half its coefficient (-11.90055419). Square it (141.6231900) and add it to both sides. Add '141.6231900' to each side of the equation. -23.80110837x + 141.6231900 + x2 = -110.0788177 + 141.6231900 Reorder the terms: 141.6231900 + -23.80110837x + x2 = -110.0788177 + 141.6231900 Combine like terms: -110.0788177 + 141.6231900 = 31.5443723 141.6231900 + -23.80110837x + x2 = 31.5443723 Factor a perfect square on the left side: (x + -11.90055419)(x + -11.90055419) = 31.5443723 Calculate the square root of the right side: 5.616437688 Break this problem into two subproblems by setting (x + -11.90055419) equal to 5.616437688 and -5.616437688.Subproblem 1
x + -11.90055419 = 5.616437688 Simplifying x + -11.90055419 = 5.616437688 Reorder the terms: -11.90055419 + x = 5.616437688 Solving -11.90055419 + x = 5.616437688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.90055419' to each side of the equation. -11.90055419 + 11.90055419 + x = 5.616437688 + 11.90055419 Combine like terms: -11.90055419 + 11.90055419 = 0.00000000 0.00000000 + x = 5.616437688 + 11.90055419 x = 5.616437688 + 11.90055419 Combine like terms: 5.616437688 + 11.90055419 = 17.516991878 x = 17.516991878 Simplifying x = 17.516991878Subproblem 2
x + -11.90055419 = -5.616437688 Simplifying x + -11.90055419 = -5.616437688 Reorder the terms: -11.90055419 + x = -5.616437688 Solving -11.90055419 + x = -5.616437688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.90055419' to each side of the equation. -11.90055419 + 11.90055419 + x = -5.616437688 + 11.90055419 Combine like terms: -11.90055419 + 11.90055419 = 0.00000000 0.00000000 + x = -5.616437688 + 11.90055419 x = -5.616437688 + 11.90055419 Combine like terms: -5.616437688 + 11.90055419 = 6.284116502 x = 6.284116502 Simplifying x = 6.284116502Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.516991878, 6.284116502}
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