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Simplifying x2 + -18x + -18 = -2 Reorder the terms: -18 + -18x + x2 = -2 Solving -18 + -18x + x2 = -2 Solving for variable 'x'. Reorder the terms: -18 + 2 + -18x + x2 = -2 + 2 Combine like terms: -18 + 2 = -16 -16 + -18x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 -16 + -18x + x2 = 0 Begin completing the square. 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 = 97 81 + -18x + x2 = 97 Factor a perfect square on the left side: (x + -9)(x + -9) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + -9) equal to 9.848857802 and -9.848857802.Subproblem 1
x + -9 = 9.848857802 Simplifying x + -9 = 9.848857802 Reorder the terms: -9 + x = 9.848857802 Solving -9 + x = 9.848857802 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 = 9.848857802 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.848857802 + 9 x = 9.848857802 + 9 Combine like terms: 9.848857802 + 9 = 18.848857802 x = 18.848857802 Simplifying x = 18.848857802Subproblem 2
x + -9 = -9.848857802 Simplifying x + -9 = -9.848857802 Reorder the terms: -9 + x = -9.848857802 Solving -9 + x = -9.848857802 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 = -9.848857802 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.848857802 + 9 x = -9.848857802 + 9 Combine like terms: -9.848857802 + 9 = -0.848857802 x = -0.848857802 Simplifying x = -0.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.848857802, -0.848857802}
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