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Simplifying (2x + 9)(2x + 21) = 425 Reorder the terms: (9 + 2x)(2x + 21) = 425 Reorder the terms: (9 + 2x)(21 + 2x) = 425 Multiply (9 + 2x) * (21 + 2x) (9(21 + 2x) + 2x * (21 + 2x)) = 425 ((21 * 9 + 2x * 9) + 2x * (21 + 2x)) = 425 ((189 + 18x) + 2x * (21 + 2x)) = 425 (189 + 18x + (21 * 2x + 2x * 2x)) = 425 (189 + 18x + (42x + 4x2)) = 425 Combine like terms: 18x + 42x = 60x (189 + 60x + 4x2) = 425 Solving 189 + 60x + 4x2 = 425 Solving for variable 'x'. Reorder the terms: 189 + -425 + 60x + 4x2 = 425 + -425 Combine like terms: 189 + -425 = -236 -236 + 60x + 4x2 = 425 + -425 Combine like terms: 425 + -425 = 0 -236 + 60x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-59 + 15x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-59 + 15x + x2)' equal to zero and attempt to solve: Simplifying -59 + 15x + x2 = 0 Solving -59 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + 15x + 59 + x2 = 0 + 59 Reorder the terms: -59 + 59 + 15x + x2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + 15x + x2 = 0 + 59 15x + x2 = 0 + 59 Combine like terms: 0 + 59 = 59 15x + x2 = 59 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 59 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 59 + 56.25 Combine like terms: 59 + 56.25 = 115.25 56.25 + 15x + x2 = 115.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 115.25 Calculate the square root of the right side: 10.735455277 Break this problem into two subproblems by setting (x + 7.5) equal to 10.735455277 and -10.735455277.Subproblem 1
x + 7.5 = 10.735455277 Simplifying x + 7.5 = 10.735455277 Reorder the terms: 7.5 + x = 10.735455277 Solving 7.5 + x = 10.735455277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 10.735455277 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 10.735455277 + -7.5 x = 10.735455277 + -7.5 Combine like terms: 10.735455277 + -7.5 = 3.235455277 x = 3.235455277 Simplifying x = 3.235455277Subproblem 2
x + 7.5 = -10.735455277 Simplifying x + 7.5 = -10.735455277 Reorder the terms: 7.5 + x = -10.735455277 Solving 7.5 + x = -10.735455277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -10.735455277 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -10.735455277 + -7.5 x = -10.735455277 + -7.5 Combine like terms: -10.735455277 + -7.5 = -18.235455277 x = -18.235455277 Simplifying x = -18.235455277Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.235455277, -18.235455277}Solution
x = {3.235455277, -18.235455277}
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