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Simplifying -1x2 + -18x + 48 = 0 Reorder the terms: 48 + -18x + -1x2 = 0 Solving 48 + -18x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 18x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 18x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 18x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 18x + x2 = 0 + 48 18x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 18x + x2 = 48 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 = 48 + 81 Reorder the terms: 81 + 18x + x2 = 48 + 81 Combine like terms: 48 + 81 = 129 81 + 18x + x2 = 129 Factor a perfect square on the left side: (x + 9)(x + 9) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + 9) equal to 11.357816692 and -11.357816692.Subproblem 1
x + 9 = 11.357816692 Simplifying x + 9 = 11.357816692 Reorder the terms: 9 + x = 11.357816692 Solving 9 + x = 11.357816692 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 = 11.357816692 + -9 Combine like terms: 9 + -9 = 0 0 + x = 11.357816692 + -9 x = 11.357816692 + -9 Combine like terms: 11.357816692 + -9 = 2.357816692 x = 2.357816692 Simplifying x = 2.357816692Subproblem 2
x + 9 = -11.357816692 Simplifying x + 9 = -11.357816692 Reorder the terms: 9 + x = -11.357816692 Solving 9 + x = -11.357816692 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 = -11.357816692 + -9 Combine like terms: 9 + -9 = 0 0 + x = -11.357816692 + -9 x = -11.357816692 + -9 Combine like terms: -11.357816692 + -9 = -20.357816692 x = -20.357816692 Simplifying x = -20.357816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.357816692, -20.357816692}
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