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Simplifying (16 + -2x)(14 + -2x) = 187 Multiply (16 + -2x) * (14 + -2x) (16(14 + -2x) + -2x * (14 + -2x)) = 187 ((14 * 16 + -2x * 16) + -2x * (14 + -2x)) = 187 ((224 + -32x) + -2x * (14 + -2x)) = 187 (224 + -32x + (14 * -2x + -2x * -2x)) = 187 (224 + -32x + (-28x + 4x2)) = 187 Combine like terms: -32x + -28x = -60x (224 + -60x + 4x2) = 187 Solving 224 + -60x + 4x2 = 187 Solving for variable 'x'. Reorder the terms: 224 + -187 + -60x + 4x2 = 187 + -187 Combine like terms: 224 + -187 = 37 37 + -60x + 4x2 = 187 + -187 Combine like terms: 187 + -187 = 0 37 + -60x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9.25 + -15x + x2 = 0 Move the constant term to the right: Add '-9.25' to each side of the equation. 9.25 + -15x + -9.25 + x2 = 0 + -9.25 Reorder the terms: 9.25 + -9.25 + -15x + x2 = 0 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + -15x + x2 = 0 + -9.25 -15x + x2 = 0 + -9.25 Combine like terms: 0 + -9.25 = -9.25 -15x + x2 = -9.25 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -9.25 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -9.25 + 56.25 Combine like terms: -9.25 + 56.25 = 47 56.25 + -15x + x2 = 47 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + -7.5) equal to 6.8556546 and -6.8556546.Subproblem 1
x + -7.5 = 6.8556546 Simplifying x + -7.5 = 6.8556546 Reorder the terms: -7.5 + x = 6.8556546 Solving -7.5 + x = 6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.8556546 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.8556546 + 7.5 x = 6.8556546 + 7.5 Combine like terms: 6.8556546 + 7.5 = 14.3556546 x = 14.3556546 Simplifying x = 14.3556546Subproblem 2
x + -7.5 = -6.8556546 Simplifying x + -7.5 = -6.8556546 Reorder the terms: -7.5 + x = -6.8556546 Solving -7.5 + x = -6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.8556546 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.8556546 + 7.5 x = -6.8556546 + 7.5 Combine like terms: -6.8556546 + 7.5 = 0.6443454 x = 0.6443454 Simplifying x = 0.6443454Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.3556546, 0.6443454}
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