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Simplifying 3x + 2x(x + -20) = 220 Reorder the terms: 3x + 2x(-20 + x) = 220 3x + (-20 * 2x + x * 2x) = 220 3x + (-40x + 2x2) = 220 Combine like terms: 3x + -40x = -37x -37x + 2x2 = 220 Solving -37x + 2x2 = 220 Solving for variable 'x'. Reorder the terms: -220 + -37x + 2x2 = 220 + -220 Combine like terms: 220 + -220 = 0 -220 + -37x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -110 + -18.5x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + -18.5x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + -18.5x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + -18.5x + x2 = 0 + 110 -18.5x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 -18.5x + x2 = 110 The x term is -18.5x. Take half its coefficient (-9.25). Square it (85.5625) and add it to both sides. Add '85.5625' to each side of the equation. -18.5x + 85.5625 + x2 = 110 + 85.5625 Reorder the terms: 85.5625 + -18.5x + x2 = 110 + 85.5625 Combine like terms: 110 + 85.5625 = 195.5625 85.5625 + -18.5x + x2 = 195.5625 Factor a perfect square on the left side: (x + -9.25)(x + -9.25) = 195.5625 Calculate the square root of the right side: 13.984366271 Break this problem into two subproblems by setting (x + -9.25) equal to 13.984366271 and -13.984366271.Subproblem 1
x + -9.25 = 13.984366271 Simplifying x + -9.25 = 13.984366271 Reorder the terms: -9.25 + x = 13.984366271 Solving -9.25 + x = 13.984366271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + x = 13.984366271 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + x = 13.984366271 + 9.25 x = 13.984366271 + 9.25 Combine like terms: 13.984366271 + 9.25 = 23.234366271 x = 23.234366271 Simplifying x = 23.234366271Subproblem 2
x + -9.25 = -13.984366271 Simplifying x + -9.25 = -13.984366271 Reorder the terms: -9.25 + x = -13.984366271 Solving -9.25 + x = -13.984366271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + x = -13.984366271 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + x = -13.984366271 + 9.25 x = -13.984366271 + 9.25 Combine like terms: -13.984366271 + 9.25 = -4.734366271 x = -4.734366271 Simplifying x = -4.734366271Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.234366271, -4.734366271}
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