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Simplifying 8x + -9 = 4x(15 + -2x) Reorder the terms: -9 + 8x = 4x(15 + -2x) -9 + 8x = (15 * 4x + -2x * 4x) -9 + 8x = (60x + -8x2) Solving -9 + 8x = 60x + -8x2 Solving for variable 'x'. Combine like terms: 8x + -60x = -52x -9 + -52x + 8x2 = 60x + -8x2 + -60x + 8x2 Reorder the terms: -9 + -52x + 8x2 = 60x + -60x + -8x2 + 8x2 Combine like terms: 60x + -60x = 0 -9 + -52x + 8x2 = 0 + -8x2 + 8x2 -9 + -52x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -9 + -52x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -6.5x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -6.5x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -6.5x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -6.5x + x2 = 0 + 1.125 -6.5x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -6.5x + x2 = 1.125 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 1.125 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 1.125 + 10.5625 Combine like terms: 1.125 + 10.5625 = 11.6875 10.5625 + -6.5x + x2 = 11.6875 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 11.6875 Calculate the square root of the right side: 3.418698583 Break this problem into two subproblems by setting (x + -3.25) equal to 3.418698583 and -3.418698583.Subproblem 1
x + -3.25 = 3.418698583 Simplifying x + -3.25 = 3.418698583 Reorder the terms: -3.25 + x = 3.418698583 Solving -3.25 + x = 3.418698583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 3.418698583 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.418698583 + 3.25 x = 3.418698583 + 3.25 Combine like terms: 3.418698583 + 3.25 = 6.668698583 x = 6.668698583 Simplifying x = 6.668698583Subproblem 2
x + -3.25 = -3.418698583 Simplifying x + -3.25 = -3.418698583 Reorder the terms: -3.25 + x = -3.418698583 Solving -3.25 + x = -3.418698583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -3.418698583 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.418698583 + 3.25 x = -3.418698583 + 3.25 Combine like terms: -3.418698583 + 3.25 = -0.168698583 x = -0.168698583 Simplifying x = -0.168698583Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.668698583, -0.168698583}
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