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Simplifying 2x2 + 3x + -612 = 0 Reorder the terms: -612 + 3x + 2x2 = 0 Solving -612 + 3x + 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'. -306 + 1.5x + x2 = 0 Move the constant term to the right: Add '306' to each side of the equation. -306 + 1.5x + 306 + x2 = 0 + 306 Reorder the terms: -306 + 306 + 1.5x + x2 = 0 + 306 Combine like terms: -306 + 306 = 0 0 + 1.5x + x2 = 0 + 306 1.5x + x2 = 0 + 306 Combine like terms: 0 + 306 = 306 1.5x + x2 = 306 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 306 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 306 + 0.5625 Combine like terms: 306 + 0.5625 = 306.5625 0.5625 + 1.5x + x2 = 306.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 306.5625 Calculate the square root of the right side: 17.508926295 Break this problem into two subproblems by setting (x + 0.75) equal to 17.508926295 and -17.508926295.Subproblem 1
x + 0.75 = 17.508926295 Simplifying x + 0.75 = 17.508926295 Reorder the terms: 0.75 + x = 17.508926295 Solving 0.75 + x = 17.508926295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 17.508926295 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 17.508926295 + -0.75 x = 17.508926295 + -0.75 Combine like terms: 17.508926295 + -0.75 = 16.758926295 x = 16.758926295 Simplifying x = 16.758926295Subproblem 2
x + 0.75 = -17.508926295 Simplifying x + 0.75 = -17.508926295 Reorder the terms: 0.75 + x = -17.508926295 Solving 0.75 + x = -17.508926295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -17.508926295 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -17.508926295 + -0.75 x = -17.508926295 + -0.75 Combine like terms: -17.508926295 + -0.75 = -18.258926295 x = -18.258926295 Simplifying x = -18.258926295Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.758926295, -18.258926295}
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