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Simplifying (9 + -2x)(16 + -2x) = 88 Multiply (9 + -2x) * (16 + -2x) (9(16 + -2x) + -2x * (16 + -2x)) = 88 ((16 * 9 + -2x * 9) + -2x * (16 + -2x)) = 88 ((144 + -18x) + -2x * (16 + -2x)) = 88 (144 + -18x + (16 * -2x + -2x * -2x)) = 88 (144 + -18x + (-32x + 4x2)) = 88 Combine like terms: -18x + -32x = -50x (144 + -50x + 4x2) = 88 Solving 144 + -50x + 4x2 = 88 Solving for variable 'x'. Reorder the terms: 144 + -88 + -50x + 4x2 = 88 + -88 Combine like terms: 144 + -88 = 56 56 + -50x + 4x2 = 88 + -88 Combine like terms: 88 + -88 = 0 56 + -50x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(28 + -25x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(28 + -25x + 2x2)' equal to zero and attempt to solve: Simplifying 28 + -25x + 2x2 = 0 Solving 28 + -25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14 + -12.5x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -12.5x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -12.5x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -12.5x + x2 = 0 + -14 -12.5x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -12.5x + x2 = -14 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -14 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -14 + 39.0625 Combine like terms: -14 + 39.0625 = 25.0625 39.0625 + -12.5x + x2 = 25.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (x + -6.25) equal to 5.006246099 and -5.006246099.Subproblem 1
x + -6.25 = 5.006246099 Simplifying x + -6.25 = 5.006246099 Reorder the terms: -6.25 + x = 5.006246099 Solving -6.25 + x = 5.006246099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 5.006246099 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 5.006246099 + 6.25 x = 5.006246099 + 6.25 Combine like terms: 5.006246099 + 6.25 = 11.256246099 x = 11.256246099 Simplifying x = 11.256246099Subproblem 2
x + -6.25 = -5.006246099 Simplifying x + -6.25 = -5.006246099 Reorder the terms: -6.25 + x = -5.006246099 Solving -6.25 + x = -5.006246099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -5.006246099 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -5.006246099 + 6.25 x = -5.006246099 + 6.25 Combine like terms: -5.006246099 + 6.25 = 1.243753901 x = 1.243753901 Simplifying x = 1.243753901Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.256246099, 1.243753901}Solution
x = {11.256246099, 1.243753901}
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