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Simplifying (2x + 60)(2x + 25) = 93080 Reorder the terms: (60 + 2x)(2x + 25) = 93080 Reorder the terms: (60 + 2x)(25 + 2x) = 93080 Multiply (60 + 2x) * (25 + 2x) (60(25 + 2x) + 2x * (25 + 2x)) = 93080 ((25 * 60 + 2x * 60) + 2x * (25 + 2x)) = 93080 ((1500 + 120x) + 2x * (25 + 2x)) = 93080 (1500 + 120x + (25 * 2x + 2x * 2x)) = 93080 (1500 + 120x + (50x + 4x2)) = 93080 Combine like terms: 120x + 50x = 170x (1500 + 170x + 4x2) = 93080 Solving 1500 + 170x + 4x2 = 93080 Solving for variable 'x'. Reorder the terms: 1500 + -93080 + 170x + 4x2 = 93080 + -93080 Combine like terms: 1500 + -93080 = -91580 -91580 + 170x + 4x2 = 93080 + -93080 Combine like terms: 93080 + -93080 = 0 -91580 + 170x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45790 + 85x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45790 + 85x + 2x2)' equal to zero and attempt to solve: Simplifying -45790 + 85x + 2x2 = 0 Solving -45790 + 85x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22895 + 42.5x + x2 = 0 Move the constant term to the right: Add '22895' to each side of the equation. -22895 + 42.5x + 22895 + x2 = 0 + 22895 Reorder the terms: -22895 + 22895 + 42.5x + x2 = 0 + 22895 Combine like terms: -22895 + 22895 = 0 0 + 42.5x + x2 = 0 + 22895 42.5x + x2 = 0 + 22895 Combine like terms: 0 + 22895 = 22895 42.5x + x2 = 22895 The x term is 42.5x. Take half its coefficient (21.25). Square it (451.5625) and add it to both sides. Add '451.5625' to each side of the equation. 42.5x + 451.5625 + x2 = 22895 + 451.5625 Reorder the terms: 451.5625 + 42.5x + x2 = 22895 + 451.5625 Combine like terms: 22895 + 451.5625 = 23346.5625 451.5625 + 42.5x + x2 = 23346.5625 Factor a perfect square on the left side: (x + 21.25)(x + 21.25) = 23346.5625 Calculate the square root of the right side: 152.795819642 Break this problem into two subproblems by setting (x + 21.25) equal to 152.795819642 and -152.795819642.Subproblem 1
x + 21.25 = 152.795819642 Simplifying x + 21.25 = 152.795819642 Reorder the terms: 21.25 + x = 152.795819642 Solving 21.25 + x = 152.795819642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.25' to each side of the equation. 21.25 + -21.25 + x = 152.795819642 + -21.25 Combine like terms: 21.25 + -21.25 = 0.00 0.00 + x = 152.795819642 + -21.25 x = 152.795819642 + -21.25 Combine like terms: 152.795819642 + -21.25 = 131.545819642 x = 131.545819642 Simplifying x = 131.545819642Subproblem 2
x + 21.25 = -152.795819642 Simplifying x + 21.25 = -152.795819642 Reorder the terms: 21.25 + x = -152.795819642 Solving 21.25 + x = -152.795819642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.25' to each side of the equation. 21.25 + -21.25 + x = -152.795819642 + -21.25 Combine like terms: 21.25 + -21.25 = 0.00 0.00 + x = -152.795819642 + -21.25 x = -152.795819642 + -21.25 Combine like terms: -152.795819642 + -21.25 = -174.045819642 x = -174.045819642 Simplifying x = -174.045819642Solution
The solution to the problem is based on the solutions from the subproblems. x = {131.545819642, -174.045819642}Solution
x = {131.545819642, -174.045819642}
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