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Simplifying 2x2 + -3x + -180 = 0 Reorder the terms: -180 + -3x + 2x2 = 0 Solving -180 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -90 + -1.5x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + -1.5x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -1.5x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -1.5x + x2 = 0 + 90 -1.5x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -1.5x + x2 = 90 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 90 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 90 + 0.5625 Combine like terms: 90 + 0.5625 = 90.5625 0.5625 + -1.5x + x2 = 90.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 90.5625 Calculate the square root of the right side: 9.516433155 Break this problem into two subproblems by setting (x + -0.75) equal to 9.516433155 and -9.516433155.Subproblem 1
x + -0.75 = 9.516433155 Simplifying x + -0.75 = 9.516433155 Reorder the terms: -0.75 + x = 9.516433155 Solving -0.75 + x = 9.516433155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 9.516433155 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 9.516433155 + 0.75 x = 9.516433155 + 0.75 Combine like terms: 9.516433155 + 0.75 = 10.266433155 x = 10.266433155 Simplifying x = 10.266433155Subproblem 2
x + -0.75 = -9.516433155 Simplifying x + -0.75 = -9.516433155 Reorder the terms: -0.75 + x = -9.516433155 Solving -0.75 + x = -9.516433155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -9.516433155 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -9.516433155 + 0.75 x = -9.516433155 + 0.75 Combine like terms: -9.516433155 + 0.75 = -8.766433155 x = -8.766433155 Simplifying x = -8.766433155Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.266433155, -8.766433155}
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