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Simplifying (72 + -2x)(60 + -2x) = 340 Multiply (72 + -2x) * (60 + -2x) (72(60 + -2x) + -2x * (60 + -2x)) = 340 ((60 * 72 + -2x * 72) + -2x * (60 + -2x)) = 340 ((4320 + -144x) + -2x * (60 + -2x)) = 340 (4320 + -144x + (60 * -2x + -2x * -2x)) = 340 (4320 + -144x + (-120x + 4x2)) = 340 Combine like terms: -144x + -120x = -264x (4320 + -264x + 4x2) = 340 Solving 4320 + -264x + 4x2 = 340 Solving for variable 'x'. Reorder the terms: 4320 + -340 + -264x + 4x2 = 340 + -340 Combine like terms: 4320 + -340 = 3980 3980 + -264x + 4x2 = 340 + -340 Combine like terms: 340 + -340 = 0 3980 + -264x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(995 + -66x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(995 + -66x + x2)' equal to zero and attempt to solve: Simplifying 995 + -66x + x2 = 0 Solving 995 + -66x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-995' to each side of the equation. 995 + -66x + -995 + x2 = 0 + -995 Reorder the terms: 995 + -995 + -66x + x2 = 0 + -995 Combine like terms: 995 + -995 = 0 0 + -66x + x2 = 0 + -995 -66x + x2 = 0 + -995 Combine like terms: 0 + -995 = -995 -66x + x2 = -995 The x term is -66x. Take half its coefficient (-33). Square it (1089) and add it to both sides. Add '1089' to each side of the equation. -66x + 1089 + x2 = -995 + 1089 Reorder the terms: 1089 + -66x + x2 = -995 + 1089 Combine like terms: -995 + 1089 = 94 1089 + -66x + x2 = 94 Factor a perfect square on the left side: (x + -33)(x + -33) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + -33) equal to 9.695359715 and -9.695359715.Subproblem 1
x + -33 = 9.695359715 Simplifying x + -33 = 9.695359715 Reorder the terms: -33 + x = 9.695359715 Solving -33 + x = 9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x = 9.695359715 + 33 Combine like terms: -33 + 33 = 0 0 + x = 9.695359715 + 33 x = 9.695359715 + 33 Combine like terms: 9.695359715 + 33 = 42.695359715 x = 42.695359715 Simplifying x = 42.695359715Subproblem 2
x + -33 = -9.695359715 Simplifying x + -33 = -9.695359715 Reorder the terms: -33 + x = -9.695359715 Solving -33 + x = -9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x = -9.695359715 + 33 Combine like terms: -33 + 33 = 0 0 + x = -9.695359715 + 33 x = -9.695359715 + 33 Combine like terms: -9.695359715 + 33 = 23.304640285 x = 23.304640285 Simplifying x = 23.304640285Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.695359715, 23.304640285}Solution
x = {42.695359715, 23.304640285}
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