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Simplifying (-2x + 3)(-1x + 15) = 15 Reorder the terms: (3 + -2x)(-1x + 15) = 15 Reorder the terms: (3 + -2x)(15 + -1x) = 15 Multiply (3 + -2x) * (15 + -1x) (3(15 + -1x) + -2x * (15 + -1x)) = 15 ((15 * 3 + -1x * 3) + -2x * (15 + -1x)) = 15 ((45 + -3x) + -2x * (15 + -1x)) = 15 (45 + -3x + (15 * -2x + -1x * -2x)) = 15 (45 + -3x + (-30x + 2x2)) = 15 Combine like terms: -3x + -30x = -33x (45 + -33x + 2x2) = 15 Solving 45 + -33x + 2x2 = 15 Solving for variable 'x'. Reorder the terms: 45 + -15 + -33x + 2x2 = 15 + -15 Combine like terms: 45 + -15 = 30 30 + -33x + 2x2 = 15 + -15 Combine like terms: 15 + -15 = 0 30 + -33x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 15 + -16.5x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -16.5x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -16.5x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -16.5x + x2 = 0 + -15 -16.5x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -16.5x + x2 = -15 The x term is -16.5x. Take half its coefficient (-8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. -16.5x + 68.0625 + x2 = -15 + 68.0625 Reorder the terms: 68.0625 + -16.5x + x2 = -15 + 68.0625 Combine like terms: -15 + 68.0625 = 53.0625 68.0625 + -16.5x + x2 = 53.0625 Factor a perfect square on the left side: (x + -8.25)(x + -8.25) = 53.0625 Calculate the square root of the right side: 7.284401142 Break this problem into two subproblems by setting (x + -8.25) equal to 7.284401142 and -7.284401142.Subproblem 1
x + -8.25 = 7.284401142 Simplifying x + -8.25 = 7.284401142 Reorder the terms: -8.25 + x = 7.284401142 Solving -8.25 + x = 7.284401142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = 7.284401142 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = 7.284401142 + 8.25 x = 7.284401142 + 8.25 Combine like terms: 7.284401142 + 8.25 = 15.534401142 x = 15.534401142 Simplifying x = 15.534401142Subproblem 2
x + -8.25 = -7.284401142 Simplifying x + -8.25 = -7.284401142 Reorder the terms: -8.25 + x = -7.284401142 Solving -8.25 + x = -7.284401142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = -7.284401142 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = -7.284401142 + 8.25 x = -7.284401142 + 8.25 Combine like terms: -7.284401142 + 8.25 = 0.965598858 x = 0.965598858 Simplifying x = 0.965598858Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.534401142, 0.965598858}
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