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Simplifying x(31 + -5 + -1x) = 10 + -3x Combine like terms: 31 + -5 = 26 x(26 + -1x) = 10 + -3x (26 * x + -1x * x) = 10 + -3x (26x + -1x2) = 10 + -3x Solving 26x + -1x2 = 10 + -3x Solving for variable 'x'. Reorder the terms: -10 + 26x + 3x + -1x2 = 10 + -3x + -10 + 3x Combine like terms: 26x + 3x = 29x -10 + 29x + -1x2 = 10 + -3x + -10 + 3x Reorder the terms: -10 + 29x + -1x2 = 10 + -10 + -3x + 3x Combine like terms: 10 + -10 = 0 -10 + 29x + -1x2 = 0 + -3x + 3x -10 + 29x + -1x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -10 + 29x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -29x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -29x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -29x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -29x + x2 = 0 + -10 -29x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -29x + x2 = -10 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -10 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -10 + 210.25 Combine like terms: -10 + 210.25 = 200.25 210.25 + -29x + x2 = 200.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (x + -14.5) equal to 14.150971698 and -14.150971698.Subproblem 1
x + -14.5 = 14.150971698 Simplifying x + -14.5 = 14.150971698 Reorder the terms: -14.5 + x = 14.150971698 Solving -14.5 + x = 14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 14.150971698 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 14.150971698 + 14.5 x = 14.150971698 + 14.5 Combine like terms: 14.150971698 + 14.5 = 28.650971698 x = 28.650971698 Simplifying x = 28.650971698Subproblem 2
x + -14.5 = -14.150971698 Simplifying x + -14.5 = -14.150971698 Reorder the terms: -14.5 + x = -14.150971698 Solving -14.5 + x = -14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -14.150971698 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -14.150971698 + 14.5 x = -14.150971698 + 14.5 Combine like terms: -14.150971698 + 14.5 = 0.349028302 x = 0.349028302 Simplifying x = 0.349028302Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.650971698, 0.349028302}
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