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Simplifying (11 + -2x)(8.5 + -2x) = 0 Multiply (11 + -2x) * (8.5 + -2x) (11(8.5 + -2x) + -2x * (8.5 + -2x)) = 0 ((8.5 * 11 + -2x * 11) + -2x * (8.5 + -2x)) = 0 ((93.5 + -22x) + -2x * (8.5 + -2x)) = 0 (93.5 + -22x + (8.5 * -2x + -2x * -2x)) = 0 (93.5 + -22x + (-17x + 4x2)) = 0 Combine like terms: -22x + -17x = -39x (93.5 + -39x + 4x2) = 0 Solving 93.5 + -39x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 23.375 + -9.75x + x2 = 0 Move the constant term to the right: Add '-23.375' to each side of the equation. 23.375 + -9.75x + -23.375 + x2 = 0 + -23.375 Reorder the terms: 23.375 + -23.375 + -9.75x + x2 = 0 + -23.375 Combine like terms: 23.375 + -23.375 = 0.000 0.000 + -9.75x + x2 = 0 + -23.375 -9.75x + x2 = 0 + -23.375 Combine like terms: 0 + -23.375 = -23.375 -9.75x + x2 = -23.375 The x term is -9.75x. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75x + 23.765625 + x2 = -23.375 + 23.765625 Reorder the terms: 23.765625 + -9.75x + x2 = -23.375 + 23.765625 Combine like terms: -23.375 + 23.765625 = 0.390625 23.765625 + -9.75x + x2 = 0.390625 Factor a perfect square on the left side: (x + -4.875)(x + -4.875) = 0.390625 Calculate the square root of the right side: 0.625 Break this problem into two subproblems by setting (x + -4.875) equal to 0.625 and -0.625.Subproblem 1
x + -4.875 = 0.625 Simplifying x + -4.875 = 0.625 Reorder the terms: -4.875 + x = 0.625 Solving -4.875 + x = 0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 0.625 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 0.625 + 4.875 x = 0.625 + 4.875 Combine like terms: 0.625 + 4.875 = 5.5 x = 5.5 Simplifying x = 5.5Subproblem 2
x + -4.875 = -0.625 Simplifying x + -4.875 = -0.625 Reorder the terms: -4.875 + x = -0.625 Solving -4.875 + x = -0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -0.625 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -0.625 + 4.875 x = -0.625 + 4.875 Combine like terms: -0.625 + 4.875 = 4.25 x = 4.25 Simplifying x = 4.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.5, 4.25}
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