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Simplifying -1(x + 3x + -2 + -7) + 3x + 5x = x(2x + 3) Reorder the terms: -1(-2 + -7 + x + 3x) + 3x + 5x = x(2x + 3) Combine like terms: -2 + -7 = -9 -1(-9 + x + 3x) + 3x + 5x = x(2x + 3) Combine like terms: x + 3x = 4x -1(-9 + 4x) + 3x + 5x = x(2x + 3) (-9 * -1 + 4x * -1) + 3x + 5x = x(2x + 3) (9 + -4x) + 3x + 5x = x(2x + 3) Combine like terms: -4x + 3x = -1x 9 + -1x + 5x = x(2x + 3) Combine like terms: -1x + 5x = 4x 9 + 4x = x(2x + 3) Reorder the terms: 9 + 4x = x(3 + 2x) 9 + 4x = (3 * x + 2x * x) 9 + 4x = (3x + 2x2) Solving 9 + 4x = 3x + 2x2 Solving for variable 'x'. Combine like terms: 4x + -3x = 1x 9 + 1x + -2x2 = 3x + 2x2 + -3x + -2x2 Reorder the terms: 9 + 1x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 9 + 1x + -2x2 = 0 + 2x2 + -2x2 9 + 1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 9 + 1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -0.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -0.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -0.5x + x2 = 0 + 4.5 -0.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -0.5x + x2 = 4.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 4.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 4.5 + 0.0625 Combine like terms: 4.5 + 0.0625 = 4.5625 0.0625 + -0.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + -0.25) equal to 2.136000936 and -2.136000936.Subproblem 1
x + -0.25 = 2.136000936 Simplifying x + -0.25 = 2.136000936 Reorder the terms: -0.25 + x = 2.136000936 Solving -0.25 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.136000936 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.136000936 + 0.25 x = 2.136000936 + 0.25 Combine like terms: 2.136000936 + 0.25 = 2.386000936 x = 2.386000936 Simplifying x = 2.386000936Subproblem 2
x + -0.25 = -2.136000936 Simplifying x + -0.25 = -2.136000936 Reorder the terms: -0.25 + x = -2.136000936 Solving -0.25 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.136000936 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.136000936 + 0.25 x = -2.136000936 + 0.25 Combine like terms: -2.136000936 + 0.25 = -1.886000936 x = -1.886000936 Simplifying x = -1.886000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.386000936, -1.886000936}
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