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Simplifying 2x2 + -2x = 170 Reorder the terms: -2x + 2x2 = 170 Solving -2x + 2x2 = 170 Solving for variable 'x'. Reorder the terms: -170 + -2x + 2x2 = 170 + -170 Combine like terms: 170 + -170 = 0 -170 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-85 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-85 + -1x + x2)' equal to zero and attempt to solve: Simplifying -85 + -1x + x2 = 0 Solving -85 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + -1x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + -1x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -1x + x2 = 0 + 85 -1x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 -1x + x2 = 85 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 85 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 85 + 0.25 Combine like terms: 85 + 0.25 = 85.25 0.25 + -1x + x2 = 85.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 85.25 Calculate the square root of the right side: 9.233092656 Break this problem into two subproblems by setting (x + -0.5) equal to 9.233092656 and -9.233092656.Subproblem 1
x + -0.5 = 9.233092656 Simplifying x + -0.5 = 9.233092656 Reorder the terms: -0.5 + x = 9.233092656 Solving -0.5 + x = 9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 9.233092656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 9.233092656 + 0.5 x = 9.233092656 + 0.5 Combine like terms: 9.233092656 + 0.5 = 9.733092656 x = 9.733092656 Simplifying x = 9.733092656Subproblem 2
x + -0.5 = -9.233092656 Simplifying x + -0.5 = -9.233092656 Reorder the terms: -0.5 + x = -9.233092656 Solving -0.5 + x = -9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -9.233092656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -9.233092656 + 0.5 x = -9.233092656 + 0.5 Combine like terms: -9.233092656 + 0.5 = -8.733092656 x = -8.733092656 Simplifying x = -8.733092656Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.733092656, -8.733092656}Solution
x = {9.733092656, -8.733092656}
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