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Simplifying 0 = x2 + -18x + 16 Reorder the terms: 0 = 16 + -18x + x2 Solving 0 = 16 + -18x + x2 Solving for variable 'x'. Combine like terms: 0 + -16 = -16 -16 + 18x + -1x2 = 16 + -18x + x2 + -16 + 18x + -1x2 Reorder the terms: -16 + 18x + -1x2 = 16 + -16 + -18x + 18x + x2 + -1x2 Combine like terms: 16 + -16 = 0 -16 + 18x + -1x2 = 0 + -18x + 18x + x2 + -1x2 -16 + 18x + -1x2 = -18x + 18x + x2 + -1x2 Combine like terms: -18x + 18x = 0 -16 + 18x + -1x2 = 0 + x2 + -1x2 -16 + 18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -16 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 16 + -18x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -18x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -18x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -18x + x2 = 0 + -16 -18x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -18x + x2 = -16 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 = -16 + 81 Reorder the terms: 81 + -18x + x2 = -16 + 81 Combine like terms: -16 + 81 = 65 81 + -18x + x2 = 65 Factor a perfect square on the left side: (x + -9)(x + -9) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + -9) equal to 8.062257748 and -8.062257748.Subproblem 1
x + -9 = 8.062257748 Simplifying x + -9 = 8.062257748 Reorder the terms: -9 + x = 8.062257748 Solving -9 + x = 8.062257748 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 = 8.062257748 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.062257748 + 9 x = 8.062257748 + 9 Combine like terms: 8.062257748 + 9 = 17.062257748 x = 17.062257748 Simplifying x = 17.062257748Subproblem 2
x + -9 = -8.062257748 Simplifying x + -9 = -8.062257748 Reorder the terms: -9 + x = -8.062257748 Solving -9 + x = -8.062257748 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 = -8.062257748 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.062257748 + 9 x = -8.062257748 + 9 Combine like terms: -8.062257748 + 9 = 0.937742252 x = 0.937742252 Simplifying x = 0.937742252Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.062257748, 0.937742252}
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