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Simplifying x2 + -5x + 4x + 36 = 180 Reorder the terms: 36 + -5x + 4x + x2 = 180 Combine like terms: -5x + 4x = -1x 36 + -1x + x2 = 180 Solving 36 + -1x + x2 = 180 Solving for variable 'x'. Reorder the terms: 36 + -180 + -1x + x2 = 180 + -180 Combine like terms: 36 + -180 = -144 -144 + -1x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -144 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -1x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -1x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -1x + x2 = 0 + 144 -1x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -1x + x2 = 144 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 = 144 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 144 + 0.25 Combine like terms: 144 + 0.25 = 144.25 0.25 + -1x + x2 = 144.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (x + -0.5) equal to 12.010412149 and -12.010412149.Subproblem 1
x + -0.5 = 12.010412149 Simplifying x + -0.5 = 12.010412149 Reorder the terms: -0.5 + x = 12.010412149 Solving -0.5 + x = 12.010412149 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 = 12.010412149 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 12.010412149 + 0.5 x = 12.010412149 + 0.5 Combine like terms: 12.010412149 + 0.5 = 12.510412149 x = 12.510412149 Simplifying x = 12.510412149Subproblem 2
x + -0.5 = -12.010412149 Simplifying x + -0.5 = -12.010412149 Reorder the terms: -0.5 + x = -12.010412149 Solving -0.5 + x = -12.010412149 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 = -12.010412149 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -12.010412149 + 0.5 x = -12.010412149 + 0.5 Combine like terms: -12.010412149 + 0.5 = -11.510412149 x = -11.510412149 Simplifying x = -11.510412149Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.510412149, -11.510412149}
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