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Simplifying (2x + 5) * x = 420 Reorder the terms: (5 + 2x) * x = 420 Reorder the terms for easier multiplication: x(5 + 2x) = 420 (5 * x + 2x * x) = 420 (5x + 2x2) = 420 Solving 5x + 2x2 = 420 Solving for variable 'x'. Reorder the terms: -420 + 5x + 2x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -210 + 2.5x + x2 = 0 Move the constant term to the right: Add '210' to each side of the equation. -210 + 2.5x + 210 + x2 = 0 + 210 Reorder the terms: -210 + 210 + 2.5x + x2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + 2.5x + x2 = 0 + 210 2.5x + x2 = 0 + 210 Combine like terms: 0 + 210 = 210 2.5x + x2 = 210 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 = 210 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 210 + 1.5625 Combine like terms: 210 + 1.5625 = 211.5625 1.5625 + 2.5x + x2 = 211.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 211.5625 Calculate the square root of the right side: 14.545188208 Break this problem into two subproblems by setting (x + 1.25) equal to 14.545188208 and -14.545188208.Subproblem 1
x + 1.25 = 14.545188208 Simplifying x + 1.25 = 14.545188208 Reorder the terms: 1.25 + x = 14.545188208 Solving 1.25 + x = 14.545188208 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 = 14.545188208 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 14.545188208 + -1.25 x = 14.545188208 + -1.25 Combine like terms: 14.545188208 + -1.25 = 13.295188208 x = 13.295188208 Simplifying x = 13.295188208Subproblem 2
x + 1.25 = -14.545188208 Simplifying x + 1.25 = -14.545188208 Reorder the terms: 1.25 + x = -14.545188208 Solving 1.25 + x = -14.545188208 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 = -14.545188208 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -14.545188208 + -1.25 x = -14.545188208 + -1.25 Combine like terms: -14.545188208 + -1.25 = -15.795188208 x = -15.795188208 Simplifying x = -15.795188208Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.295188208, -15.795188208}
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