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Simplifying (2x + 72)(2x + -20) = 180 Reorder the terms: (72 + 2x)(2x + -20) = 180 Reorder the terms: (72 + 2x)(-20 + 2x) = 180 Multiply (72 + 2x) * (-20 + 2x) (72(-20 + 2x) + 2x * (-20 + 2x)) = 180 ((-20 * 72 + 2x * 72) + 2x * (-20 + 2x)) = 180 ((-1440 + 144x) + 2x * (-20 + 2x)) = 180 (-1440 + 144x + (-20 * 2x + 2x * 2x)) = 180 (-1440 + 144x + (-40x + 4x2)) = 180 Combine like terms: 144x + -40x = 104x (-1440 + 104x + 4x2) = 180 Solving -1440 + 104x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -1440 + -180 + 104x + 4x2 = 180 + -180 Combine like terms: -1440 + -180 = -1620 -1620 + 104x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -1620 + 104x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-405 + 26x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-405 + 26x + x2)' equal to zero and attempt to solve: Simplifying -405 + 26x + x2 = 0 Solving -405 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '405' to each side of the equation. -405 + 26x + 405 + x2 = 0 + 405 Reorder the terms: -405 + 405 + 26x + x2 = 0 + 405 Combine like terms: -405 + 405 = 0 0 + 26x + x2 = 0 + 405 26x + x2 = 0 + 405 Combine like terms: 0 + 405 = 405 26x + x2 = 405 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = 405 + 169 Reorder the terms: 169 + 26x + x2 = 405 + 169 Combine like terms: 405 + 169 = 574 169 + 26x + x2 = 574 Factor a perfect square on the left side: (x + 13)(x + 13) = 574 Calculate the square root of the right side: 23.958297101 Break this problem into two subproblems by setting (x + 13) equal to 23.958297101 and -23.958297101.Subproblem 1
x + 13 = 23.958297101 Simplifying x + 13 = 23.958297101 Reorder the terms: 13 + x = 23.958297101 Solving 13 + x = 23.958297101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 23.958297101 + -13 Combine like terms: 13 + -13 = 0 0 + x = 23.958297101 + -13 x = 23.958297101 + -13 Combine like terms: 23.958297101 + -13 = 10.958297101 x = 10.958297101 Simplifying x = 10.958297101Subproblem 2
x + 13 = -23.958297101 Simplifying x + 13 = -23.958297101 Reorder the terms: 13 + x = -23.958297101 Solving 13 + x = -23.958297101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -23.958297101 + -13 Combine like terms: 13 + -13 = 0 0 + x = -23.958297101 + -13 x = -23.958297101 + -13 Combine like terms: -23.958297101 + -13 = -36.958297101 x = -36.958297101 Simplifying x = -36.958297101Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.958297101, -36.958297101}Solution
x = {10.958297101, -36.958297101}
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