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Simplifying (4x + -7)(x + 16) = 68 Reorder the terms: (-7 + 4x)(x + 16) = 68 Reorder the terms: (-7 + 4x)(16 + x) = 68 Multiply (-7 + 4x) * (16 + x) (-7(16 + x) + 4x * (16 + x)) = 68 ((16 * -7 + x * -7) + 4x * (16 + x)) = 68 ((-112 + -7x) + 4x * (16 + x)) = 68 (-112 + -7x + (16 * 4x + x * 4x)) = 68 (-112 + -7x + (64x + 4x2)) = 68 Combine like terms: -7x + 64x = 57x (-112 + 57x + 4x2) = 68 Solving -112 + 57x + 4x2 = 68 Solving for variable 'x'. Reorder the terms: -112 + -68 + 57x + 4x2 = 68 + -68 Combine like terms: -112 + -68 = -180 -180 + 57x + 4x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -180 + 57x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -45 + 14.25x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 14.25x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 14.25x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 14.25x + x2 = 0 + 45 14.25x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 14.25x + x2 = 45 The x term is 14.25x. Take half its coefficient (7.125). Square it (50.765625) and add it to both sides. Add '50.765625' to each side of the equation. 14.25x + 50.765625 + x2 = 45 + 50.765625 Reorder the terms: 50.765625 + 14.25x + x2 = 45 + 50.765625 Combine like terms: 45 + 50.765625 = 95.765625 50.765625 + 14.25x + x2 = 95.765625 Factor a perfect square on the left side: (x + 7.125)(x + 7.125) = 95.765625 Calculate the square root of the right side: 9.785991263 Break this problem into two subproblems by setting (x + 7.125) equal to 9.785991263 and -9.785991263.Subproblem 1
x + 7.125 = 9.785991263 Simplifying x + 7.125 = 9.785991263 Reorder the terms: 7.125 + x = 9.785991263 Solving 7.125 + x = 9.785991263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.125' to each side of the equation. 7.125 + -7.125 + x = 9.785991263 + -7.125 Combine like terms: 7.125 + -7.125 = 0.000 0.000 + x = 9.785991263 + -7.125 x = 9.785991263 + -7.125 Combine like terms: 9.785991263 + -7.125 = 2.660991263 x = 2.660991263 Simplifying x = 2.660991263Subproblem 2
x + 7.125 = -9.785991263 Simplifying x + 7.125 = -9.785991263 Reorder the terms: 7.125 + x = -9.785991263 Solving 7.125 + x = -9.785991263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.125' to each side of the equation. 7.125 + -7.125 + x = -9.785991263 + -7.125 Combine like terms: 7.125 + -7.125 = 0.000 0.000 + x = -9.785991263 + -7.125 x = -9.785991263 + -7.125 Combine like terms: -9.785991263 + -7.125 = -16.910991263 x = -16.910991263 Simplifying x = -16.910991263Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.660991263, -16.910991263}
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