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Simplifying -0.5x2 + 20x + 230 = 0 Reorder the terms: 230 + 20x + -0.5x2 = 0 Solving 230 + 20x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -460 + -40x + x2 = 0 Move the constant term to the right: Add '460' to each side of the equation. -460 + -40x + 460 + x2 = 0 + 460 Reorder the terms: -460 + 460 + -40x + x2 = 0 + 460 Combine like terms: -460 + 460 = 0 0 + -40x + x2 = 0 + 460 -40x + x2 = 0 + 460 Combine like terms: 0 + 460 = 460 -40x + x2 = 460 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 460 + 400 Reorder the terms: 400 + -40x + x2 = 460 + 400 Combine like terms: 460 + 400 = 860 400 + -40x + x2 = 860 Factor a perfect square on the left side: (x + -20)(x + -20) = 860 Calculate the square root of the right side: 29.325756597 Break this problem into two subproblems by setting (x + -20) equal to 29.325756597 and -29.325756597.Subproblem 1
x + -20 = 29.325756597 Simplifying x + -20 = 29.325756597 Reorder the terms: -20 + x = 29.325756597 Solving -20 + x = 29.325756597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 29.325756597 + 20 Combine like terms: -20 + 20 = 0 0 + x = 29.325756597 + 20 x = 29.325756597 + 20 Combine like terms: 29.325756597 + 20 = 49.325756597 x = 49.325756597 Simplifying x = 49.325756597Subproblem 2
x + -20 = -29.325756597 Simplifying x + -20 = -29.325756597 Reorder the terms: -20 + x = -29.325756597 Solving -20 + x = -29.325756597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -29.325756597 + 20 Combine like terms: -20 + 20 = 0 0 + x = -29.325756597 + 20 x = -29.325756597 + 20 Combine like terms: -29.325756597 + 20 = -9.325756597 x = -9.325756597 Simplifying x = -9.325756597Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.325756597, -9.325756597}
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