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Simplifying x(2x + 5) = 100 Reorder the terms: x(5 + 2x) = 100 (5 * x + 2x * x) = 100 (5x + 2x2) = 100 Solving 5x + 2x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 5x + 2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50 + 2.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 2.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 2.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 2.5x + x2 = 0 + 50 2.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 2.5x + x2 = 50 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 = 50 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 50 + 1.5625 Combine like terms: 50 + 1.5625 = 51.5625 1.5625 + 2.5x + x2 = 51.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 51.5625 Calculate the square root of the right side: 7.180703308 Break this problem into two subproblems by setting (x + 1.25) equal to 7.180703308 and -7.180703308.Subproblem 1
x + 1.25 = 7.180703308 Simplifying x + 1.25 = 7.180703308 Reorder the terms: 1.25 + x = 7.180703308 Solving 1.25 + x = 7.180703308 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 = 7.180703308 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 7.180703308 + -1.25 x = 7.180703308 + -1.25 Combine like terms: 7.180703308 + -1.25 = 5.930703308 x = 5.930703308 Simplifying x = 5.930703308Subproblem 2
x + 1.25 = -7.180703308 Simplifying x + 1.25 = -7.180703308 Reorder the terms: 1.25 + x = -7.180703308 Solving 1.25 + x = -7.180703308 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 = -7.180703308 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -7.180703308 + -1.25 x = -7.180703308 + -1.25 Combine like terms: -7.180703308 + -1.25 = -8.430703308 x = -8.430703308 Simplifying x = -8.430703308Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.930703308, -8.430703308}
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