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Simplifying (20 + -2x)(14 + -2x) = 116 Multiply (20 + -2x) * (14 + -2x) (20(14 + -2x) + -2x * (14 + -2x)) = 116 ((14 * 20 + -2x * 20) + -2x * (14 + -2x)) = 116 ((280 + -40x) + -2x * (14 + -2x)) = 116 (280 + -40x + (14 * -2x + -2x * -2x)) = 116 (280 + -40x + (-28x + 4x2)) = 116 Combine like terms: -40x + -28x = -68x (280 + -68x + 4x2) = 116 Solving 280 + -68x + 4x2 = 116 Solving for variable 'x'. Reorder the terms: 280 + -116 + -68x + 4x2 = 116 + -116 Combine like terms: 280 + -116 = 164 164 + -68x + 4x2 = 116 + -116 Combine like terms: 116 + -116 = 0 164 + -68x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(41 + -17x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(41 + -17x + x2)' equal to zero and attempt to solve: Simplifying 41 + -17x + x2 = 0 Solving 41 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -17x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + -17x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -17x + x2 = 0 + -41 -17x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 -17x + x2 = -41 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -41 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -41 + 72.25 Combine like terms: -41 + 72.25 = 31.25 72.25 + -17x + x2 = 31.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + -8.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + -8.5 = 5.590169944 Simplifying x + -8.5 = 5.590169944 Reorder the terms: -8.5 + x = 5.590169944 Solving -8.5 + x = 5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 5.590169944 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 5.590169944 + 8.5 x = 5.590169944 + 8.5 Combine like terms: 5.590169944 + 8.5 = 14.090169944 x = 14.090169944 Simplifying x = 14.090169944Subproblem 2
x + -8.5 = -5.590169944 Simplifying x + -8.5 = -5.590169944 Reorder the terms: -8.5 + x = -5.590169944 Solving -8.5 + x = -5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -5.590169944 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -5.590169944 + 8.5 x = -5.590169944 + 8.5 Combine like terms: -5.590169944 + 8.5 = 2.909830056 x = 2.909830056 Simplifying x = 2.909830056Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.090169944, 2.909830056}Solution
x = {14.090169944, 2.909830056}
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