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Simplifying x2 + -8x + 6 + 3x + -12 + -128 = 0 Reorder the terms: 6 + -12 + -128 + -8x + 3x + x2 = 0 Combine like terms: 6 + -12 = -6 -6 + -128 + -8x + 3x + x2 = 0 Combine like terms: -6 + -128 = -134 -134 + -8x + 3x + x2 = 0 Combine like terms: -8x + 3x = -5x -134 + -5x + x2 = 0 Solving -134 + -5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '134' to each side of the equation. -134 + -5x + 134 + x2 = 0 + 134 Reorder the terms: -134 + 134 + -5x + x2 = 0 + 134 Combine like terms: -134 + 134 = 0 0 + -5x + x2 = 0 + 134 -5x + x2 = 0 + 134 Combine like terms: 0 + 134 = 134 -5x + x2 = 134 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 134 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 134 + 6.25 Combine like terms: 134 + 6.25 = 140.25 6.25 + -5x + x2 = 140.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (x + -2.5) equal to 11.842719282 and -11.842719282.Subproblem 1
x + -2.5 = 11.842719282 Simplifying x + -2.5 = 11.842719282 Reorder the terms: -2.5 + x = 11.842719282 Solving -2.5 + x = 11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 11.842719282 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 11.842719282 + 2.5 x = 11.842719282 + 2.5 Combine like terms: 11.842719282 + 2.5 = 14.342719282 x = 14.342719282 Simplifying x = 14.342719282Subproblem 2
x + -2.5 = -11.842719282 Simplifying x + -2.5 = -11.842719282 Reorder the terms: -2.5 + x = -11.842719282 Solving -2.5 + x = -11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -11.842719282 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -11.842719282 + 2.5 x = -11.842719282 + 2.5 Combine like terms: -11.842719282 + 2.5 = -9.342719282 x = -9.342719282 Simplifying x = -9.342719282Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.342719282, -9.342719282}
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