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Simplifying x2 + -2x = 10x + 140 Reorder the terms: -2x + x2 = 10x + 140 Reorder the terms: -2x + x2 = 140 + 10x Solving -2x + x2 = 140 + 10x Solving for variable 'x'. Reorder the terms: -140 + -2x + -10x + x2 = 140 + 10x + -140 + -10x Combine like terms: -2x + -10x = -12x -140 + -12x + x2 = 140 + 10x + -140 + -10x Reorder the terms: -140 + -12x + x2 = 140 + -140 + 10x + -10x Combine like terms: 140 + -140 = 0 -140 + -12x + x2 = 0 + 10x + -10x -140 + -12x + x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -140 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + -12x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -12x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -12x + x2 = 0 + 140 -12x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -12x + x2 = 140 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 = 140 + 36 Reorder the terms: 36 + -12x + x2 = 140 + 36 Combine like terms: 140 + 36 = 176 36 + -12x + x2 = 176 Factor a perfect square on the left side: (x + -6)(x + -6) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (x + -6) equal to 13.266499161 and -13.266499161.Subproblem 1
x + -6 = 13.266499161 Simplifying x + -6 = 13.266499161 Reorder the terms: -6 + x = 13.266499161 Solving -6 + x = 13.266499161 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 = 13.266499161 + 6 Combine like terms: -6 + 6 = 0 0 + x = 13.266499161 + 6 x = 13.266499161 + 6 Combine like terms: 13.266499161 + 6 = 19.266499161 x = 19.266499161 Simplifying x = 19.266499161Subproblem 2
x + -6 = -13.266499161 Simplifying x + -6 = -13.266499161 Reorder the terms: -6 + x = -13.266499161 Solving -6 + x = -13.266499161 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 = -13.266499161 + 6 Combine like terms: -6 + 6 = 0 0 + x = -13.266499161 + 6 x = -13.266499161 + 6 Combine like terms: -13.266499161 + 6 = -7.266499161 x = -7.266499161 Simplifying x = -7.266499161Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.266499161, -7.266499161}
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