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Simplifying (2x + 25)(2x + 10) = 304 Reorder the terms: (25 + 2x)(2x + 10) = 304 Reorder the terms: (25 + 2x)(10 + 2x) = 304 Multiply (25 + 2x) * (10 + 2x) (25(10 + 2x) + 2x * (10 + 2x)) = 304 ((10 * 25 + 2x * 25) + 2x * (10 + 2x)) = 304 ((250 + 50x) + 2x * (10 + 2x)) = 304 (250 + 50x + (10 * 2x + 2x * 2x)) = 304 (250 + 50x + (20x + 4x2)) = 304 Combine like terms: 50x + 20x = 70x (250 + 70x + 4x2) = 304 Solving 250 + 70x + 4x2 = 304 Solving for variable 'x'. Reorder the terms: 250 + -304 + 70x + 4x2 = 304 + -304 Combine like terms: 250 + -304 = -54 -54 + 70x + 4x2 = 304 + -304 Combine like terms: 304 + -304 = 0 -54 + 70x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 35x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + 35x + 2x2)' equal to zero and attempt to solve: Simplifying -27 + 35x + 2x2 = 0 Solving -27 + 35x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + 17.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 17.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 17.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 17.5x + x2 = 0 + 13.5 17.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 17.5x + x2 = 13.5 The x term is 17.5x. Take half its coefficient (8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. 17.5x + 76.5625 + x2 = 13.5 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 13.5 + 76.5625 Combine like terms: 13.5 + 76.5625 = 90.0625 76.5625 + 17.5x + x2 = 90.0625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 90.0625 Calculate the square root of the right side: 9.490126448 Break this problem into two subproblems by setting (x + 8.75) equal to 9.490126448 and -9.490126448.Subproblem 1
x + 8.75 = 9.490126448 Simplifying x + 8.75 = 9.490126448 Reorder the terms: 8.75 + x = 9.490126448 Solving 8.75 + x = 9.490126448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 9.490126448 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 9.490126448 + -8.75 x = 9.490126448 + -8.75 Combine like terms: 9.490126448 + -8.75 = 0.740126448 x = 0.740126448 Simplifying x = 0.740126448Subproblem 2
x + 8.75 = -9.490126448 Simplifying x + 8.75 = -9.490126448 Reorder the terms: 8.75 + x = -9.490126448 Solving 8.75 + x = -9.490126448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -9.490126448 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -9.490126448 + -8.75 x = -9.490126448 + -8.75 Combine like terms: -9.490126448 + -8.75 = -18.240126448 x = -18.240126448 Simplifying x = -18.240126448Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.740126448, -18.240126448}Solution
x = {0.740126448, -18.240126448}
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