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Simplifying 3x2 + -2x + 15x + -10 = x2 + -3x + -3x + 9 Reorder the terms: -10 + -2x + 15x + 3x2 = x2 + -3x + -3x + 9 Combine like terms: -2x + 15x = 13x -10 + 13x + 3x2 = x2 + -3x + -3x + 9 Reorder the terms: -10 + 13x + 3x2 = 9 + -3x + -3x + x2 Combine like terms: -3x + -3x = -6x -10 + 13x + 3x2 = 9 + -6x + x2 Solving -10 + 13x + 3x2 = 9 + -6x + x2 Solving for variable 'x'. Reorder the terms: -10 + -9 + 13x + 6x + 3x2 + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Combine like terms: -10 + -9 = -19 -19 + 13x + 6x + 3x2 + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Combine like terms: 13x + 6x = 19x -19 + 19x + 3x2 + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -19 + 19x + 2x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Reorder the terms: -19 + 19x + 2x2 = 9 + -9 + -6x + 6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 -19 + 19x + 2x2 = 0 + -6x + 6x + x2 + -1x2 -19 + 19x + 2x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 -19 + 19x + 2x2 = 0 + x2 + -1x2 -19 + 19x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -19 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 9.5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 9.5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 9.5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 9.5x + x2 = 0 + 9.5 9.5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 9.5x + x2 = 9.5 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 = 9.5 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 9.5 + 22.5625 Combine like terms: 9.5 + 22.5625 = 32.0625 22.5625 + 9.5x + x2 = 32.0625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 32.0625 Calculate the square root of the right side: 5.662375826 Break this problem into two subproblems by setting (x + 4.75) equal to 5.662375826 and -5.662375826.Subproblem 1
x + 4.75 = 5.662375826 Simplifying x + 4.75 = 5.662375826 Reorder the terms: 4.75 + x = 5.662375826 Solving 4.75 + x = 5.662375826 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 = 5.662375826 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 5.662375826 + -4.75 x = 5.662375826 + -4.75 Combine like terms: 5.662375826 + -4.75 = 0.912375826 x = 0.912375826 Simplifying x = 0.912375826Subproblem 2
x + 4.75 = -5.662375826 Simplifying x + 4.75 = -5.662375826 Reorder the terms: 4.75 + x = -5.662375826 Solving 4.75 + x = -5.662375826 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 = -5.662375826 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -5.662375826 + -4.75 x = -5.662375826 + -4.75 Combine like terms: -5.662375826 + -4.75 = -10.412375826 x = -10.412375826 Simplifying x = -10.412375826Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.912375826, -10.412375826}
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