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Simplifying -1x2 + 18x + 100 = 0 Reorder the terms: 100 + 18x + -1x2 = 0 Solving 100 + 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'. -100 + -18x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -18x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -18x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -18x + x2 = 0 + 100 -18x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -18x + x2 = 100 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 = 100 + 81 Reorder the terms: 81 + -18x + x2 = 100 + 81 Combine like terms: 100 + 81 = 181 81 + -18x + x2 = 181 Factor a perfect square on the left side: (x + -9)(x + -9) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (x + -9) equal to 13.453624047 and -13.453624047.Subproblem 1
x + -9 = 13.453624047 Simplifying x + -9 = 13.453624047 Reorder the terms: -9 + x = 13.453624047 Solving -9 + x = 13.453624047 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 = 13.453624047 + 9 Combine like terms: -9 + 9 = 0 0 + x = 13.453624047 + 9 x = 13.453624047 + 9 Combine like terms: 13.453624047 + 9 = 22.453624047 x = 22.453624047 Simplifying x = 22.453624047Subproblem 2
x + -9 = -13.453624047 Simplifying x + -9 = -13.453624047 Reorder the terms: -9 + x = -13.453624047 Solving -9 + x = -13.453624047 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 = -13.453624047 + 9 Combine like terms: -9 + 9 = 0 0 + x = -13.453624047 + 9 x = -13.453624047 + 9 Combine like terms: -13.453624047 + 9 = -4.453624047 x = -4.453624047 Simplifying x = -4.453624047Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.453624047, -4.453624047}
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