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Simplifying (2x + 5)(2x + 25) = 231 Reorder the terms: (5 + 2x)(2x + 25) = 231 Reorder the terms: (5 + 2x)(25 + 2x) = 231 Multiply (5 + 2x) * (25 + 2x) (5(25 + 2x) + 2x * (25 + 2x)) = 231 ((25 * 5 + 2x * 5) + 2x * (25 + 2x)) = 231 ((125 + 10x) + 2x * (25 + 2x)) = 231 (125 + 10x + (25 * 2x + 2x * 2x)) = 231 (125 + 10x + (50x + 4x2)) = 231 Combine like terms: 10x + 50x = 60x (125 + 60x + 4x2) = 231 Solving 125 + 60x + 4x2 = 231 Solving for variable 'x'. Reorder the terms: 125 + -231 + 60x + 4x2 = 231 + -231 Combine like terms: 125 + -231 = -106 -106 + 60x + 4x2 = 231 + -231 Combine like terms: 231 + -231 = 0 -106 + 60x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-53 + 30x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-53 + 30x + 2x2)' equal to zero and attempt to solve: Simplifying -53 + 30x + 2x2 = 0 Solving -53 + 30x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -26.5 + 15x + x2 = 0 Move the constant term to the right: Add '26.5' to each side of the equation. -26.5 + 15x + 26.5 + x2 = 0 + 26.5 Reorder the terms: -26.5 + 26.5 + 15x + x2 = 0 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + 15x + x2 = 0 + 26.5 15x + x2 = 0 + 26.5 Combine like terms: 0 + 26.5 = 26.5 15x + x2 = 26.5 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 = 26.5 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 26.5 + 56.25 Combine like terms: 26.5 + 56.25 = 82.75 56.25 + 15x + x2 = 82.75 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 82.75 Calculate the square root of the right side: 9.096702699 Break this problem into two subproblems by setting (x + 7.5) equal to 9.096702699 and -9.096702699.Subproblem 1
x + 7.5 = 9.096702699 Simplifying x + 7.5 = 9.096702699 Reorder the terms: 7.5 + x = 9.096702699 Solving 7.5 + x = 9.096702699 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 = 9.096702699 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.096702699 + -7.5 x = 9.096702699 + -7.5 Combine like terms: 9.096702699 + -7.5 = 1.596702699 x = 1.596702699 Simplifying x = 1.596702699Subproblem 2
x + 7.5 = -9.096702699 Simplifying x + 7.5 = -9.096702699 Reorder the terms: 7.5 + x = -9.096702699 Solving 7.5 + x = -9.096702699 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 = -9.096702699 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.096702699 + -7.5 x = -9.096702699 + -7.5 Combine like terms: -9.096702699 + -7.5 = -16.596702699 x = -16.596702699 Simplifying x = -16.596702699Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.596702699, -16.596702699}Solution
x = {1.596702699, -16.596702699}
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