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Simplifying x2 + -10 = 2x + 132 Reorder the terms: -10 + x2 = 2x + 132 Reorder the terms: -10 + x2 = 132 + 2x Solving -10 + x2 = 132 + 2x Solving for variable 'x'. Reorder the terms: -10 + -132 + -2x + x2 = 132 + 2x + -132 + -2x Combine like terms: -10 + -132 = -142 -142 + -2x + x2 = 132 + 2x + -132 + -2x Reorder the terms: -142 + -2x + x2 = 132 + -132 + 2x + -2x Combine like terms: 132 + -132 = 0 -142 + -2x + x2 = 0 + 2x + -2x -142 + -2x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -142 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '142' to each side of the equation. -142 + -2x + 142 + x2 = 0 + 142 Reorder the terms: -142 + 142 + -2x + x2 = 0 + 142 Combine like terms: -142 + 142 = 0 0 + -2x + x2 = 0 + 142 -2x + x2 = 0 + 142 Combine like terms: 0 + 142 = 142 -2x + x2 = 142 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 142 + 1 Reorder the terms: 1 + -2x + x2 = 142 + 1 Combine like terms: 142 + 1 = 143 1 + -2x + x2 = 143 Factor a perfect square on the left side: (x + -1)(x + -1) = 143 Calculate the square root of the right side: 11.958260743 Break this problem into two subproblems by setting (x + -1) equal to 11.958260743 and -11.958260743.Subproblem 1
x + -1 = 11.958260743 Simplifying x + -1 = 11.958260743 Reorder the terms: -1 + x = 11.958260743 Solving -1 + x = 11.958260743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 11.958260743 + 1 Combine like terms: -1 + 1 = 0 0 + x = 11.958260743 + 1 x = 11.958260743 + 1 Combine like terms: 11.958260743 + 1 = 12.958260743 x = 12.958260743 Simplifying x = 12.958260743Subproblem 2
x + -1 = -11.958260743 Simplifying x + -1 = -11.958260743 Reorder the terms: -1 + x = -11.958260743 Solving -1 + x = -11.958260743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -11.958260743 + 1 Combine like terms: -1 + 1 = 0 0 + x = -11.958260743 + 1 x = -11.958260743 + 1 Combine like terms: -11.958260743 + 1 = -10.958260743 x = -10.958260743 Simplifying x = -10.958260743Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.958260743, -10.958260743}
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