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Simplifying (2x + 60)(4x + 20) = 180 Reorder the terms: (60 + 2x)(4x + 20) = 180 Reorder the terms: (60 + 2x)(20 + 4x) = 180 Multiply (60 + 2x) * (20 + 4x) (60(20 + 4x) + 2x * (20 + 4x)) = 180 ((20 * 60 + 4x * 60) + 2x * (20 + 4x)) = 180 ((1200 + 240x) + 2x * (20 + 4x)) = 180 (1200 + 240x + (20 * 2x + 4x * 2x)) = 180 (1200 + 240x + (40x + 8x2)) = 180 Combine like terms: 240x + 40x = 280x (1200 + 280x + 8x2) = 180 Solving 1200 + 280x + 8x2 = 180 Solving for variable 'x'. Reorder the terms: 1200 + -180 + 280x + 8x2 = 180 + -180 Combine like terms: 1200 + -180 = 1020 1020 + 280x + 8x2 = 180 + -180 Combine like terms: 180 + -180 = 0 1020 + 280x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(255 + 70x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(255 + 70x + 2x2)' equal to zero and attempt to solve: Simplifying 255 + 70x + 2x2 = 0 Solving 255 + 70x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 127.5 + 35x + x2 = 0 Move the constant term to the right: Add '-127.5' to each side of the equation. 127.5 + 35x + -127.5 + x2 = 0 + -127.5 Reorder the terms: 127.5 + -127.5 + 35x + x2 = 0 + -127.5 Combine like terms: 127.5 + -127.5 = 0.0 0.0 + 35x + x2 = 0 + -127.5 35x + x2 = 0 + -127.5 Combine like terms: 0 + -127.5 = -127.5 35x + x2 = -127.5 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = -127.5 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -127.5 + 306.25 Combine like terms: -127.5 + 306.25 = 178.75 306.25 + 35x + x2 = 178.75 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 178.75 Calculate the square root of the right side: 13.369741957 Break this problem into two subproblems by setting (x + 17.5) equal to 13.369741957 and -13.369741957.Subproblem 1
x + 17.5 = 13.369741957 Simplifying x + 17.5 = 13.369741957 Reorder the terms: 17.5 + x = 13.369741957 Solving 17.5 + x = 13.369741957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 13.369741957 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 13.369741957 + -17.5 x = 13.369741957 + -17.5 Combine like terms: 13.369741957 + -17.5 = -4.130258043 x = -4.130258043 Simplifying x = -4.130258043Subproblem 2
x + 17.5 = -13.369741957 Simplifying x + 17.5 = -13.369741957 Reorder the terms: 17.5 + x = -13.369741957 Solving 17.5 + x = -13.369741957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -13.369741957 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -13.369741957 + -17.5 x = -13.369741957 + -17.5 Combine like terms: -13.369741957 + -17.5 = -30.869741957 x = -30.869741957 Simplifying x = -30.869741957Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.130258043, -30.869741957}Solution
x = {-4.130258043, -30.869741957}
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