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Simplifying 2x2 + -3x + 101 = 360 Reorder the terms: 101 + -3x + 2x2 = 360 Solving 101 + -3x + 2x2 = 360 Solving for variable 'x'. Reorder the terms: 101 + -360 + -3x + 2x2 = 360 + -360 Combine like terms: 101 + -360 = -259 -259 + -3x + 2x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -259 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -129.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '129.5' to each side of the equation. -129.5 + -1.5x + 129.5 + x2 = 0 + 129.5 Reorder the terms: -129.5 + 129.5 + -1.5x + x2 = 0 + 129.5 Combine like terms: -129.5 + 129.5 = 0.0 0.0 + -1.5x + x2 = 0 + 129.5 -1.5x + x2 = 0 + 129.5 Combine like terms: 0 + 129.5 = 129.5 -1.5x + x2 = 129.5 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 = 129.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 129.5 + 0.5625 Combine like terms: 129.5 + 0.5625 = 130.0625 0.5625 + -1.5x + x2 = 130.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 130.0625 Calculate the square root of the right side: 11.404494728 Break this problem into two subproblems by setting (x + -0.75) equal to 11.404494728 and -11.404494728.Subproblem 1
x + -0.75 = 11.404494728 Simplifying x + -0.75 = 11.404494728 Reorder the terms: -0.75 + x = 11.404494728 Solving -0.75 + x = 11.404494728 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 = 11.404494728 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 11.404494728 + 0.75 x = 11.404494728 + 0.75 Combine like terms: 11.404494728 + 0.75 = 12.154494728 x = 12.154494728 Simplifying x = 12.154494728Subproblem 2
x + -0.75 = -11.404494728 Simplifying x + -0.75 = -11.404494728 Reorder the terms: -0.75 + x = -11.404494728 Solving -0.75 + x = -11.404494728 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 = -11.404494728 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -11.404494728 + 0.75 x = -11.404494728 + 0.75 Combine like terms: -11.404494728 + 0.75 = -10.654494728 x = -10.654494728 Simplifying x = -10.654494728Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.154494728, -10.654494728}
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