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Simplifying (11 + -2x)(20 + -2x) = 80 Multiply (11 + -2x) * (20 + -2x) (11(20 + -2x) + -2x * (20 + -2x)) = 80 ((20 * 11 + -2x * 11) + -2x * (20 + -2x)) = 80 ((220 + -22x) + -2x * (20 + -2x)) = 80 (220 + -22x + (20 * -2x + -2x * -2x)) = 80 (220 + -22x + (-40x + 4x2)) = 80 Combine like terms: -22x + -40x = -62x (220 + -62x + 4x2) = 80 Solving 220 + -62x + 4x2 = 80 Solving for variable 'x'. Reorder the terms: 220 + -80 + -62x + 4x2 = 80 + -80 Combine like terms: 220 + -80 = 140 140 + -62x + 4x2 = 80 + -80 Combine like terms: 80 + -80 = 0 140 + -62x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(70 + -31x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(70 + -31x + 2x2)' equal to zero and attempt to solve: Simplifying 70 + -31x + 2x2 = 0 Solving 70 + -31x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 35 + -15.5x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + -15.5x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -15.5x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -15.5x + x2 = 0 + -35 -15.5x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -15.5x + x2 = -35 The x term is -15.5x. Take half its coefficient (-7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. -15.5x + 60.0625 + x2 = -35 + 60.0625 Reorder the terms: 60.0625 + -15.5x + x2 = -35 + 60.0625 Combine like terms: -35 + 60.0625 = 25.0625 60.0625 + -15.5x + x2 = 25.0625 Factor a perfect square on the left side: (x + -7.75)(x + -7.75) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (x + -7.75) equal to 5.006246099 and -5.006246099.Subproblem 1
x + -7.75 = 5.006246099 Simplifying x + -7.75 = 5.006246099 Reorder the terms: -7.75 + x = 5.006246099 Solving -7.75 + x = 5.006246099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = 5.006246099 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = 5.006246099 + 7.75 x = 5.006246099 + 7.75 Combine like terms: 5.006246099 + 7.75 = 12.756246099 x = 12.756246099 Simplifying x = 12.756246099Subproblem 2
x + -7.75 = -5.006246099 Simplifying x + -7.75 = -5.006246099 Reorder the terms: -7.75 + x = -5.006246099 Solving -7.75 + x = -5.006246099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = -5.006246099 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = -5.006246099 + 7.75 x = -5.006246099 + 7.75 Combine like terms: -5.006246099 + 7.75 = 2.743753901 x = 2.743753901 Simplifying x = 2.743753901Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.756246099, 2.743753901}Solution
x = {12.756246099, 2.743753901}
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