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Simplifying 35 + -1(2x + 9) = 2x(x + 8) + x Reorder the terms: 35 + -1(9 + 2x) = 2x(x + 8) + x 35 + (9 * -1 + 2x * -1) = 2x(x + 8) + x 35 + (-9 + -2x) = 2x(x + 8) + x Combine like terms: 35 + -9 = 26 26 + -2x = 2x(x + 8) + x Reorder the terms: 26 + -2x = 2x(8 + x) + x 26 + -2x = (8 * 2x + x * 2x) + x 26 + -2x = (16x + 2x2) + x Reorder the terms: 26 + -2x = 16x + x + 2x2 Combine like terms: 16x + x = 17x 26 + -2x = 17x + 2x2 Solving 26 + -2x = 17x + 2x2 Solving for variable 'x'. Combine like terms: -2x + -17x = -19x 26 + -19x + -2x2 = 17x + 2x2 + -17x + -2x2 Reorder the terms: 26 + -19x + -2x2 = 17x + -17x + 2x2 + -2x2 Combine like terms: 17x + -17x = 0 26 + -19x + -2x2 = 0 + 2x2 + -2x2 26 + -19x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 26 + -19x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -13 + 9.5x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 9.5x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 9.5x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 9.5x + x2 = 0 + 13 9.5x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 9.5x + x2 = 13 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 13 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 13 + 22.5625 Combine like terms: 13 + 22.5625 = 35.5625 22.5625 + 9.5x + x2 = 35.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 35.5625 Calculate the square root of the right side: 5.963430221 Break this problem into two subproblems by setting (x + 4.75) equal to 5.963430221 and -5.963430221.Subproblem 1
x + 4.75 = 5.963430221 Simplifying x + 4.75 = 5.963430221 Reorder the terms: 4.75 + x = 5.963430221 Solving 4.75 + x = 5.963430221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 5.963430221 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 5.963430221 + -4.75 x = 5.963430221 + -4.75 Combine like terms: 5.963430221 + -4.75 = 1.213430221 x = 1.213430221 Simplifying x = 1.213430221Subproblem 2
x + 4.75 = -5.963430221 Simplifying x + 4.75 = -5.963430221 Reorder the terms: 4.75 + x = -5.963430221 Solving 4.75 + x = -5.963430221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -5.963430221 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -5.963430221 + -4.75 x = -5.963430221 + -4.75 Combine like terms: -5.963430221 + -4.75 = -10.713430221 x = -10.713430221 Simplifying x = -10.713430221Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.213430221, -10.713430221}
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