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Simplifying 2x2 + x + -612 = 0 Reorder the terms: -612 + x + 2x2 = 0 Solving -612 + x + 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 + 0.5x + x2 = 0 Move the constant term to the right: Add '306' to each side of the equation. -306 + 0.5x + 306 + x2 = 0 + 306 Reorder the terms: -306 + 306 + 0.5x + x2 = 0 + 306 Combine like terms: -306 + 306 = 0 0 + 0.5x + x2 = 0 + 306 0.5x + x2 = 0 + 306 Combine like terms: 0 + 306 = 306 0.5x + x2 = 306 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 306 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 306 + 0.25 Combine like terms: 306 + 0.25 = 306.25 0.25 + 0.5x + x2 = 306.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 306.25 Calculate the square root of the right side: 17.5 Break this problem into two subproblems by setting (x + 0.5) equal to 17.5 and -17.5.Subproblem 1
x + 0.5 = 17.5 Simplifying x + 0.5 = 17.5 Reorder the terms: 0.5 + x = 17.5 Solving 0.5 + x = 17.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 17.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 17.5 + -0.5 x = 17.5 + -0.5 Combine like terms: 17.5 + -0.5 = 17 x = 17 Simplifying x = 17Subproblem 2
x + 0.5 = -17.5 Simplifying x + 0.5 = -17.5 Reorder the terms: 0.5 + x = -17.5 Solving 0.5 + x = -17.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -17.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -17.5 + -0.5 x = -17.5 + -0.5 Combine like terms: -17.5 + -0.5 = -18 x = -18 Simplifying x = -18Solution
The solution to the problem is based on the solutions from the subproblems. x = {17, -18}
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