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Simplifying x2 + -10x = 2x + 132 Reorder the terms: -10x + x2 = 2x + 132 Reorder the terms: -10x + x2 = 132 + 2x Solving -10x + x2 = 132 + 2x Solving for variable 'x'. Reorder the terms: -132 + -10x + -2x + x2 = 132 + 2x + -132 + -2x Combine like terms: -10x + -2x = -12x -132 + -12x + x2 = 132 + 2x + -132 + -2x Reorder the terms: -132 + -12x + x2 = 132 + -132 + 2x + -2x Combine like terms: 132 + -132 = 0 -132 + -12x + x2 = 0 + 2x + -2x -132 + -12x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -132 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '132' to each side of the equation. -132 + -12x + 132 + x2 = 0 + 132 Reorder the terms: -132 + 132 + -12x + x2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + -12x + x2 = 0 + 132 -12x + x2 = 0 + 132 Combine like terms: 0 + 132 = 132 -12x + x2 = 132 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 132 + 36 Reorder the terms: 36 + -12x + x2 = 132 + 36 Combine like terms: 132 + 36 = 168 36 + -12x + x2 = 168 Factor a perfect square on the left side: (x + -6)(x + -6) = 168 Calculate the square root of the right side: 12.961481397 Break this problem into two subproblems by setting (x + -6) equal to 12.961481397 and -12.961481397.Subproblem 1
x + -6 = 12.961481397 Simplifying x + -6 = 12.961481397 Reorder the terms: -6 + x = 12.961481397 Solving -6 + x = 12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 12.961481397 + 6 Combine like terms: -6 + 6 = 0 0 + x = 12.961481397 + 6 x = 12.961481397 + 6 Combine like terms: 12.961481397 + 6 = 18.961481397 x = 18.961481397 Simplifying x = 18.961481397Subproblem 2
x + -6 = -12.961481397 Simplifying x + -6 = -12.961481397 Reorder the terms: -6 + x = -12.961481397 Solving -6 + x = -12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -12.961481397 + 6 Combine like terms: -6 + 6 = 0 0 + x = -12.961481397 + 6 x = -12.961481397 + 6 Combine like terms: -12.961481397 + 6 = -6.961481397 x = -6.961481397 Simplifying x = -6.961481397Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.961481397, -6.961481397}
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