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Simplifying 1x2 + -8x + 1x2 + 10 = 180 Reorder the terms: 10 + -8x + 1x2 + 1x2 = 180 Combine like terms: 1x2 + 1x2 = 2x2 10 + -8x + 2x2 = 180 Solving 10 + -8x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 10 + -180 + -8x + 2x2 = 180 + -180 Combine like terms: 10 + -180 = -170 -170 + -8x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -170 + -8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-85 + -4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-85 + -4x + x2)' equal to zero and attempt to solve: Simplifying -85 + -4x + x2 = 0 Solving -85 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + -4x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + -4x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -4x + x2 = 0 + 85 -4x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 -4x + x2 = 85 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 85 + 4 Reorder the terms: 4 + -4x + x2 = 85 + 4 Combine like terms: 85 + 4 = 89 4 + -4x + x2 = 89 Factor a perfect square on the left side: (x + -2)(x + -2) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + -2) equal to 9.433981132 and -9.433981132.Subproblem 1
x + -2 = 9.433981132 Simplifying x + -2 = 9.433981132 Reorder the terms: -2 + x = 9.433981132 Solving -2 + x = 9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 9.433981132 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.433981132 + 2 x = 9.433981132 + 2 Combine like terms: 9.433981132 + 2 = 11.433981132 x = 11.433981132 Simplifying x = 11.433981132Subproblem 2
x + -2 = -9.433981132 Simplifying x + -2 = -9.433981132 Reorder the terms: -2 + x = -9.433981132 Solving -2 + x = -9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -9.433981132 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.433981132 + 2 x = -9.433981132 + 2 Combine like terms: -9.433981132 + 2 = -7.433981132 x = -7.433981132 Simplifying x = -7.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.433981132, -7.433981132}Solution
x = {11.433981132, -7.433981132}
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