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Simplifying 0.5x2 + -9x + -20 = 0 Reorder the terms: -20 + -9x + 0.5x2 = 0 Solving -20 + -9x + 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'. -40 + -18x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -18x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -18x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -18x + x2 = 0 + 40 -18x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -18x + x2 = 40 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 40 + 81 Reorder the terms: 81 + -18x + x2 = 40 + 81 Combine like terms: 40 + 81 = 121 81 + -18x + x2 = 121 Factor a perfect square on the left side: (x + -9)(x + -9) = 121 Calculate the square root of the right side: 11 Break this problem into two subproblems by setting (x + -9) equal to 11 and -11.Subproblem 1
x + -9 = 11 Simplifying x + -9 = 11 Reorder the terms: -9 + x = 11 Solving -9 + x = 11 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 11 + 9 Combine like terms: -9 + 9 = 0 0 + x = 11 + 9 x = 11 + 9 Combine like terms: 11 + 9 = 20 x = 20 Simplifying x = 20Subproblem 2
x + -9 = -11 Simplifying x + -9 = -11 Reorder the terms: -9 + x = -11 Solving -9 + x = -11 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -11 + 9 Combine like terms: -9 + 9 = 0 0 + x = -11 + 9 x = -11 + 9 Combine like terms: -11 + 9 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -2}
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