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Simplifying 144 = x(x + -1) Reorder the terms: 144 = x(-1 + x) 144 = (-1 * x + x * x) 144 = (-1x + x2) Solving 144 = -1x + x2 Solving for variable 'x'. Reorder the terms: 144 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 144 + x + -1x2 = 0 + x2 + -1x2 144 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 144 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -144 + -1x + x2 = 0 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 x. 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 = 11.510412149 x = 11.510412149 Simplifying x = 11.510412149Subproblem 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 = -12.510412149 x = -12.510412149 Simplifying x = -12.510412149Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.510412149, -12.510412149}
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