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Simplifying (2x + 5)(x) = 460 Reorder the terms: (5 + 2x)(x) = 460 Reorder the terms for easier multiplication: x(5 + 2x) = 460 (5 * x + 2x * x) = 460 (5x + 2x2) = 460 Solving 5x + 2x2 = 460 Solving for variable 'x'. Reorder the terms: -460 + 5x + 2x2 = 460 + -460 Combine like terms: 460 + -460 = 0 -460 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -230 + 2.5x + x2 = 0 Move the constant term to the right: Add '230' to each side of the equation. -230 + 2.5x + 230 + x2 = 0 + 230 Reorder the terms: -230 + 230 + 2.5x + x2 = 0 + 230 Combine like terms: -230 + 230 = 0 0 + 2.5x + x2 = 0 + 230 2.5x + x2 = 0 + 230 Combine like terms: 0 + 230 = 230 2.5x + x2 = 230 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 230 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 230 + 1.5625 Combine like terms: 230 + 1.5625 = 231.5625 1.5625 + 2.5x + x2 = 231.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 231.5625 Calculate the square root of the right side: 15.217177794 Break this problem into two subproblems by setting (x + 1.25) equal to 15.217177794 and -15.217177794.Subproblem 1
x + 1.25 = 15.217177794 Simplifying x + 1.25 = 15.217177794 Reorder the terms: 1.25 + x = 15.217177794 Solving 1.25 + x = 15.217177794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 15.217177794 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 15.217177794 + -1.25 x = 15.217177794 + -1.25 Combine like terms: 15.217177794 + -1.25 = 13.967177794 x = 13.967177794 Simplifying x = 13.967177794Subproblem 2
x + 1.25 = -15.217177794 Simplifying x + 1.25 = -15.217177794 Reorder the terms: 1.25 + x = -15.217177794 Solving 1.25 + x = -15.217177794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -15.217177794 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -15.217177794 + -1.25 x = -15.217177794 + -1.25 Combine like terms: -15.217177794 + -1.25 = -16.467177794 x = -16.467177794 Simplifying x = -16.467177794Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.967177794, -16.467177794}
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