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Simplifying x(x + 62) = 31250 Reorder the terms: x(62 + x) = 31250 (62 * x + x * x) = 31250 (62x + x2) = 31250 Solving 62x + x2 = 31250 Solving for variable 'x'. Reorder the terms: -31250 + 62x + x2 = 31250 + -31250 Combine like terms: 31250 + -31250 = 0 -31250 + 62x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '31250' to each side of the equation. -31250 + 62x + 31250 + x2 = 0 + 31250 Reorder the terms: -31250 + 31250 + 62x + x2 = 0 + 31250 Combine like terms: -31250 + 31250 = 0 0 + 62x + x2 = 0 + 31250 62x + x2 = 0 + 31250 Combine like terms: 0 + 31250 = 31250 62x + x2 = 31250 The x term is 62x. Take half its coefficient (31). Square it (961) and add it to both sides. Add '961' to each side of the equation. 62x + 961 + x2 = 31250 + 961 Reorder the terms: 961 + 62x + x2 = 31250 + 961 Combine like terms: 31250 + 961 = 32211 961 + 62x + x2 = 32211 Factor a perfect square on the left side: (x + 31)(x + 31) = 32211 Calculate the square root of the right side: 179.474232134 Break this problem into two subproblems by setting (x + 31) equal to 179.474232134 and -179.474232134.Subproblem 1
x + 31 = 179.474232134 Simplifying x + 31 = 179.474232134 Reorder the terms: 31 + x = 179.474232134 Solving 31 + x = 179.474232134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = 179.474232134 + -31 Combine like terms: 31 + -31 = 0 0 + x = 179.474232134 + -31 x = 179.474232134 + -31 Combine like terms: 179.474232134 + -31 = 148.474232134 x = 148.474232134 Simplifying x = 148.474232134Subproblem 2
x + 31 = -179.474232134 Simplifying x + 31 = -179.474232134 Reorder the terms: 31 + x = -179.474232134 Solving 31 + x = -179.474232134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = -179.474232134 + -31 Combine like terms: 31 + -31 = 0 0 + x = -179.474232134 + -31 x = -179.474232134 + -31 Combine like terms: -179.474232134 + -31 = -210.474232134 x = -210.474232134 Simplifying x = -210.474232134Solution
The solution to the problem is based on the solutions from the subproblems. x = {148.474232134, -210.474232134}
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