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Simplifying 180 + -1x = 46(90 + -2x2) 180 + -1x = (90 * 46 + -2x2 * 46) 180 + -1x = (4140 + -92x2) Solving 180 + -1x = 4140 + -92x2 Solving for variable 'x'. Reorder the terms: 180 + -4140 + -1x + 92x2 = 4140 + -92x2 + -4140 + 92x2 Combine like terms: 180 + -4140 = -3960 -3960 + -1x + 92x2 = 4140 + -92x2 + -4140 + 92x2 Reorder the terms: -3960 + -1x + 92x2 = 4140 + -4140 + -92x2 + 92x2 Combine like terms: 4140 + -4140 = 0 -3960 + -1x + 92x2 = 0 + -92x2 + 92x2 -3960 + -1x + 92x2 = -92x2 + 92x2 Combine like terms: -92x2 + 92x2 = 0 -3960 + -1x + 92x2 = 0 Begin completing the square. Divide all terms by 92 the coefficient of the squared term: Divide each side by '92'. -43.04347826 + -0.01086956522x + x2 = 0 Move the constant term to the right: Add '43.04347826' to each side of the equation. -43.04347826 + -0.01086956522x + 43.04347826 + x2 = 0 + 43.04347826 Reorder the terms: -43.04347826 + 43.04347826 + -0.01086956522x + x2 = 0 + 43.04347826 Combine like terms: -43.04347826 + 43.04347826 = 0.00000000 0.00000000 + -0.01086956522x + x2 = 0 + 43.04347826 -0.01086956522x + x2 = 0 + 43.04347826 Combine like terms: 0 + 43.04347826 = 43.04347826 -0.01086956522x + x2 = 43.04347826 The x term is -0.01086956522x. Take half its coefficient (-0.00543478261). Square it (0.00002953686202) and add it to both sides. Add '0.00002953686202' to each side of the equation. -0.01086956522x + 0.00002953686202 + x2 = 43.04347826 + 0.00002953686202 Reorder the terms: 0.00002953686202 + -0.01086956522x + x2 = 43.04347826 + 0.00002953686202 Combine like terms: 43.04347826 + 0.00002953686202 = 43.04350779686202 0.00002953686202 + -0.01086956522x + x2 = 43.04350779686202 Factor a perfect square on the left side: (x + -0.00543478261)(x + -0.00543478261) = 43.04350779686202 Calculate the square root of the right side: 6.560755124 Break this problem into two subproblems by setting (x + -0.00543478261) equal to 6.560755124 and -6.560755124.Subproblem 1
x + -0.00543478261 = 6.560755124 Simplifying x + -0.00543478261 = 6.560755124 Reorder the terms: -0.00543478261 + x = 6.560755124 Solving -0.00543478261 + x = 6.560755124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00543478261' to each side of the equation. -0.00543478261 + 0.00543478261 + x = 6.560755124 + 0.00543478261 Combine like terms: -0.00543478261 + 0.00543478261 = 0.00000000000 0.00000000000 + x = 6.560755124 + 0.00543478261 x = 6.560755124 + 0.00543478261 Combine like terms: 6.560755124 + 0.00543478261 = 6.56618990661 x = 6.56618990661 Simplifying x = 6.56618990661Subproblem 2
x + -0.00543478261 = -6.560755124 Simplifying x + -0.00543478261 = -6.560755124 Reorder the terms: -0.00543478261 + x = -6.560755124 Solving -0.00543478261 + x = -6.560755124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00543478261' to each side of the equation. -0.00543478261 + 0.00543478261 + x = -6.560755124 + 0.00543478261 Combine like terms: -0.00543478261 + 0.00543478261 = 0.00000000000 0.00000000000 + x = -6.560755124 + 0.00543478261 x = -6.560755124 + 0.00543478261 Combine like terms: -6.560755124 + 0.00543478261 = -6.55532034139 x = -6.55532034139 Simplifying x = -6.55532034139Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.56618990661, -6.55532034139}
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