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Simplifying 18 + 16x + -1x2 = 0 Solving 18 + 16x + -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'. -18 + -16x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -16x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -16x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -16x + x2 = 0 + 18 -16x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -16x + x2 = 18 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 18 + 64 Reorder the terms: 64 + -16x + x2 = 18 + 64 Combine like terms: 18 + 64 = 82 64 + -16x + x2 = 82 Factor a perfect square on the left side: (x + -8)(x + -8) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (x + -8) equal to 9.055385138 and -9.055385138.Subproblem 1
x + -8 = 9.055385138 Simplifying x + -8 = 9.055385138 Reorder the terms: -8 + x = 9.055385138 Solving -8 + x = 9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 9.055385138 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.055385138 + 8 x = 9.055385138 + 8 Combine like terms: 9.055385138 + 8 = 17.055385138 x = 17.055385138 Simplifying x = 17.055385138Subproblem 2
x + -8 = -9.055385138 Simplifying x + -8 = -9.055385138 Reorder the terms: -8 + x = -9.055385138 Solving -8 + x = -9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -9.055385138 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.055385138 + 8 x = -9.055385138 + 8 Combine like terms: -9.055385138 + 8 = -1.055385138 x = -1.055385138 Simplifying x = -1.055385138Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.055385138, -1.055385138}
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