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Simplifying x(5 + 2x) = 532 (5 * x + 2x * x) = 532 (5x + 2x2) = 532 Solving 5x + 2x2 = 532 Solving for variable 'x'. Reorder the terms: -532 + 5x + 2x2 = 532 + -532 Combine like terms: 532 + -532 = 0 -532 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -266 + 2.5x + x2 = 0 Move the constant term to the right: Add '266' to each side of the equation. -266 + 2.5x + 266 + x2 = 0 + 266 Reorder the terms: -266 + 266 + 2.5x + x2 = 0 + 266 Combine like terms: -266 + 266 = 0 0 + 2.5x + x2 = 0 + 266 2.5x + x2 = 0 + 266 Combine like terms: 0 + 266 = 266 2.5x + x2 = 266 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 = 266 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 266 + 1.5625 Combine like terms: 266 + 1.5625 = 267.5625 1.5625 + 2.5x + x2 = 267.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 267.5625 Calculate the square root of the right side: 16.357337803 Break this problem into two subproblems by setting (x + 1.25) equal to 16.357337803 and -16.357337803.Subproblem 1
x + 1.25 = 16.357337803 Simplifying x + 1.25 = 16.357337803 Reorder the terms: 1.25 + x = 16.357337803 Solving 1.25 + x = 16.357337803 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 = 16.357337803 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 16.357337803 + -1.25 x = 16.357337803 + -1.25 Combine like terms: 16.357337803 + -1.25 = 15.107337803 x = 15.107337803 Simplifying x = 15.107337803Subproblem 2
x + 1.25 = -16.357337803 Simplifying x + 1.25 = -16.357337803 Reorder the terms: 1.25 + x = -16.357337803 Solving 1.25 + x = -16.357337803 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 = -16.357337803 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -16.357337803 + -1.25 x = -16.357337803 + -1.25 Combine like terms: -16.357337803 + -1.25 = -17.607337803 x = -17.607337803 Simplifying x = -17.607337803Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.107337803, -17.607337803}
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