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Simplifying -1x2 + 18x = 10 Reorder the terms: 18x + -1x2 = 10 Solving 18x + -1x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 18x + -1x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -18x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -18x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -18x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -18x + x2 = 0 + -10 -18x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -18x + x2 = -10 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 = -10 + 81 Reorder the terms: 81 + -18x + x2 = -10 + 81 Combine like terms: -10 + 81 = 71 81 + -18x + x2 = 71 Factor a perfect square on the left side: (x + -9)(x + -9) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + -9) equal to 8.426149773 and -8.426149773.Subproblem 1
x + -9 = 8.426149773 Simplifying x + -9 = 8.426149773 Reorder the terms: -9 + x = 8.426149773 Solving -9 + x = 8.426149773 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 = 8.426149773 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.426149773 + 9 x = 8.426149773 + 9 Combine like terms: 8.426149773 + 9 = 17.426149773 x = 17.426149773 Simplifying x = 17.426149773Subproblem 2
x + -9 = -8.426149773 Simplifying x + -9 = -8.426149773 Reorder the terms: -9 + x = -8.426149773 Solving -9 + x = -8.426149773 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 = -8.426149773 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.426149773 + 9 x = -8.426149773 + 9 Combine like terms: -8.426149773 + 9 = 0.573850227 x = 0.573850227 Simplifying x = 0.573850227Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.426149773, 0.573850227}
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