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Simplifying 60 = (20 + -2x)(26 + -2x) Multiply (20 + -2x) * (26 + -2x) 60 = (20(26 + -2x) + -2x * (26 + -2x)) 60 = ((26 * 20 + -2x * 20) + -2x * (26 + -2x)) 60 = ((520 + -40x) + -2x * (26 + -2x)) 60 = (520 + -40x + (26 * -2x + -2x * -2x)) 60 = (520 + -40x + (-52x + 4x2)) Combine like terms: -40x + -52x = -92x 60 = (520 + -92x + 4x2) Solving 60 = 520 + -92x + 4x2 Solving for variable 'x'. Combine like terms: 60 + -520 = -460 -460 + 92x + -4x2 = 520 + -92x + 4x2 + -520 + 92x + -4x2 Reorder the terms: -460 + 92x + -4x2 = 520 + -520 + -92x + 92x + 4x2 + -4x2 Combine like terms: 520 + -520 = 0 -460 + 92x + -4x2 = 0 + -92x + 92x + 4x2 + -4x2 -460 + 92x + -4x2 = -92x + 92x + 4x2 + -4x2 Combine like terms: -92x + 92x = 0 -460 + 92x + -4x2 = 0 + 4x2 + -4x2 -460 + 92x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -460 + 92x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-115 + 23x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-115 + 23x + -1x2)' equal to zero and attempt to solve: Simplifying -115 + 23x + -1x2 = 0 Solving -115 + 23x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 115 + -23x + x2 = 0 Move the constant term to the right: Add '-115' to each side of the equation. 115 + -23x + -115 + x2 = 0 + -115 Reorder the terms: 115 + -115 + -23x + x2 = 0 + -115 Combine like terms: 115 + -115 = 0 0 + -23x + x2 = 0 + -115 -23x + x2 = 0 + -115 Combine like terms: 0 + -115 = -115 -23x + x2 = -115 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -115 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -115 + 132.25 Combine like terms: -115 + 132.25 = 17.25 132.25 + -23x + x2 = 17.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + -11.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + -11.5 = 4.153311931 Simplifying x + -11.5 = 4.153311931 Reorder the terms: -11.5 + x = 4.153311931 Solving -11.5 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 4.153311931 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 4.153311931 + 11.5 x = 4.153311931 + 11.5 Combine like terms: 4.153311931 + 11.5 = 15.653311931 x = 15.653311931 Simplifying x = 15.653311931Subproblem 2
x + -11.5 = -4.153311931 Simplifying x + -11.5 = -4.153311931 Reorder the terms: -11.5 + x = -4.153311931 Solving -11.5 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -4.153311931 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -4.153311931 + 11.5 x = -4.153311931 + 11.5 Combine like terms: -4.153311931 + 11.5 = 7.346688069 x = 7.346688069 Simplifying x = 7.346688069Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.653311931, 7.346688069}Solution
x = {15.653311931, 7.346688069}
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