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Simplifying 2x2 + 5x + -204 = 0 Reorder the terms: -204 + 5x + 2x2 = 0 Solving -204 + 5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -102 + 2.5x + x2 = 0 Move the constant term to the right: Add '102' to each side of the equation. -102 + 2.5x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + 2.5x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + 2.5x + x2 = 0 + 102 2.5x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 2.5x + x2 = 102 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 = 102 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 102 + 1.5625 Combine like terms: 102 + 1.5625 = 103.5625 1.5625 + 2.5x + x2 = 103.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 103.5625 Calculate the square root of the right side: 10.176566219 Break this problem into two subproblems by setting (x + 1.25) equal to 10.176566219 and -10.176566219.Subproblem 1
x + 1.25 = 10.176566219 Simplifying x + 1.25 = 10.176566219 Reorder the terms: 1.25 + x = 10.176566219 Solving 1.25 + x = 10.176566219 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 = 10.176566219 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 10.176566219 + -1.25 x = 10.176566219 + -1.25 Combine like terms: 10.176566219 + -1.25 = 8.926566219 x = 8.926566219 Simplifying x = 8.926566219Subproblem 2
x + 1.25 = -10.176566219 Simplifying x + 1.25 = -10.176566219 Reorder the terms: 1.25 + x = -10.176566219 Solving 1.25 + x = -10.176566219 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 = -10.176566219 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -10.176566219 + -1.25 x = -10.176566219 + -1.25 Combine like terms: -10.176566219 + -1.25 = -11.426566219 x = -11.426566219 Simplifying x = -11.426566219Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.926566219, -11.426566219}
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