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Simplifying 0 = 2x2 + -6x + -1136 Reorder the terms: 0 = -1136 + -6x + 2x2 Solving 0 = -1136 + -6x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 1136 = 1136 1136 + 6x + -2x2 = -1136 + -6x + 2x2 + 1136 + 6x + -2x2 Reorder the terms: 1136 + 6x + -2x2 = -1136 + 1136 + -6x + 6x + 2x2 + -2x2 Combine like terms: -1136 + 1136 = 0 1136 + 6x + -2x2 = 0 + -6x + 6x + 2x2 + -2x2 1136 + 6x + -2x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 1136 + 6x + -2x2 = 0 + 2x2 + -2x2 1136 + 6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1136 + 6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(568 + 3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(568 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying 568 + 3x + -1x2 = 0 Solving 568 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -568 + -3x + x2 = 0 Move the constant term to the right: Add '568' to each side of the equation. -568 + -3x + 568 + x2 = 0 + 568 Reorder the terms: -568 + 568 + -3x + x2 = 0 + 568 Combine like terms: -568 + 568 = 0 0 + -3x + x2 = 0 + 568 -3x + x2 = 0 + 568 Combine like terms: 0 + 568 = 568 -3x + x2 = 568 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 568 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 568 + 2.25 Combine like terms: 568 + 2.25 = 570.25 2.25 + -3x + x2 = 570.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 570.25 Calculate the square root of the right side: 23.879907873 Break this problem into two subproblems by setting (x + -1.5) equal to 23.879907873 and -23.879907873.Subproblem 1
x + -1.5 = 23.879907873 Simplifying x + -1.5 = 23.879907873 Reorder the terms: -1.5 + x = 23.879907873 Solving -1.5 + x = 23.879907873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 23.879907873 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 23.879907873 + 1.5 x = 23.879907873 + 1.5 Combine like terms: 23.879907873 + 1.5 = 25.379907873 x = 25.379907873 Simplifying x = 25.379907873Subproblem 2
x + -1.5 = -23.879907873 Simplifying x + -1.5 = -23.879907873 Reorder the terms: -1.5 + x = -23.879907873 Solving -1.5 + x = -23.879907873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -23.879907873 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -23.879907873 + 1.5 x = -23.879907873 + 1.5 Combine like terms: -23.879907873 + 1.5 = -22.379907873 x = -22.379907873 Simplifying x = -22.379907873Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.379907873, -22.379907873}Solution
x = {25.379907873, -22.379907873}
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