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Simplifying x2 + -18x + -16 = 25 Reorder the terms: -16 + -18x + x2 = 25 Solving -16 + -18x + x2 = 25 Solving for variable 'x'. Reorder the terms: -16 + -25 + -18x + x2 = 25 + -25 Combine like terms: -16 + -25 = -41 -41 + -18x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -41 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -18x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + -18x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -18x + x2 = 0 + 41 -18x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 -18x + x2 = 41 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 = 41 + 81 Reorder the terms: 81 + -18x + x2 = 41 + 81 Combine like terms: 41 + 81 = 122 81 + -18x + x2 = 122 Factor a perfect square on the left side: (x + -9)(x + -9) = 122 Calculate the square root of the right side: 11.045361017 Break this problem into two subproblems by setting (x + -9) equal to 11.045361017 and -11.045361017.Subproblem 1
x + -9 = 11.045361017 Simplifying x + -9 = 11.045361017 Reorder the terms: -9 + x = 11.045361017 Solving -9 + x = 11.045361017 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 = 11.045361017 + 9 Combine like terms: -9 + 9 = 0 0 + x = 11.045361017 + 9 x = 11.045361017 + 9 Combine like terms: 11.045361017 + 9 = 20.045361017 x = 20.045361017 Simplifying x = 20.045361017Subproblem 2
x + -9 = -11.045361017 Simplifying x + -9 = -11.045361017 Reorder the terms: -9 + x = -11.045361017 Solving -9 + x = -11.045361017 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 = -11.045361017 + 9 Combine like terms: -9 + 9 = 0 0 + x = -11.045361017 + 9 x = -11.045361017 + 9 Combine like terms: -11.045361017 + 9 = -2.045361017 x = -2.045361017 Simplifying x = -2.045361017Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.045361017, -2.045361017}
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