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Simplifying x(34 + x) = (-35 + 2x) (34 * x + x * x) = (-35 + 2x) (34x + x2) = (-35 + 2x) Remove parenthesis around (-35 + 2x) 34x + x2 = -35 + 2x Solving 34x + x2 = -35 + 2x Solving for variable 'x'. Reorder the terms: 35 + 34x + -2x + x2 = -35 + 2x + 35 + -2x Combine like terms: 34x + -2x = 32x 35 + 32x + x2 = -35 + 2x + 35 + -2x Reorder the terms: 35 + 32x + x2 = -35 + 35 + 2x + -2x Combine like terms: -35 + 35 = 0 35 + 32x + x2 = 0 + 2x + -2x 35 + 32x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 35 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 32x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + 32x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 32x + x2 = 0 + -35 32x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 32x + x2 = -35 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -35 + 256 Reorder the terms: 256 + 32x + x2 = -35 + 256 Combine like terms: -35 + 256 = 221 256 + 32x + x2 = 221 Factor a perfect square on the left side: (x + 16)(x + 16) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (x + 16) equal to 14.866068747 and -14.866068747.Subproblem 1
x + 16 = 14.866068747 Simplifying x + 16 = 14.866068747 Reorder the terms: 16 + x = 14.866068747 Solving 16 + x = 14.866068747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 14.866068747 + -16 Combine like terms: 16 + -16 = 0 0 + x = 14.866068747 + -16 x = 14.866068747 + -16 Combine like terms: 14.866068747 + -16 = -1.133931253 x = -1.133931253 Simplifying x = -1.133931253Subproblem 2
x + 16 = -14.866068747 Simplifying x + 16 = -14.866068747 Reorder the terms: 16 + x = -14.866068747 Solving 16 + x = -14.866068747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -14.866068747 + -16 Combine like terms: 16 + -16 = 0 0 + x = -14.866068747 + -16 x = -14.866068747 + -16 Combine like terms: -14.866068747 + -16 = -30.866068747 x = -30.866068747 Simplifying x = -30.866068747Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.133931253, -30.866068747}
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