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Simplifying x(2x + 5) = 220 Reorder the terms: x(5 + 2x) = 220 (5 * x + 2x * x) = 220 (5x + 2x2) = 220 Solving 5x + 2x2 = 220 Solving for variable 'x'. Reorder the terms: -220 + 5x + 2x2 = 220 + -220 Combine like terms: 220 + -220 = 0 -220 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -110 + 2.5x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + 2.5x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 2.5x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 2.5x + x2 = 0 + 110 2.5x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 2.5x + x2 = 110 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 = 110 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 110 + 1.5625 Combine like terms: 110 + 1.5625 = 111.5625 1.5625 + 2.5x + x2 = 111.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 111.5625 Calculate the square root of the right side: 10.562315087 Break this problem into two subproblems by setting (x + 1.25) equal to 10.562315087 and -10.562315087.Subproblem 1
x + 1.25 = 10.562315087 Simplifying x + 1.25 = 10.562315087 Reorder the terms: 1.25 + x = 10.562315087 Solving 1.25 + x = 10.562315087 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 = 10.562315087 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 10.562315087 + -1.25 x = 10.562315087 + -1.25 Combine like terms: 10.562315087 + -1.25 = 9.312315087 x = 9.312315087 Simplifying x = 9.312315087Subproblem 2
x + 1.25 = -10.562315087 Simplifying x + 1.25 = -10.562315087 Reorder the terms: 1.25 + x = -10.562315087 Solving 1.25 + x = -10.562315087 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 = -10.562315087 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -10.562315087 + -1.25 x = -10.562315087 + -1.25 Combine like terms: -10.562315087 + -1.25 = -11.812315087 x = -11.812315087 Simplifying x = -11.812315087Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.312315087, -11.812315087}
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