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Simplifying x2 + -18x + -13 = 0 Reorder the terms: -13 + -18x + x2 = 0 Solving -13 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -18x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -18x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -18x + x2 = 0 + 13 -18x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -18x + x2 = 13 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 = 13 + 81 Reorder the terms: 81 + -18x + x2 = 13 + 81 Combine like terms: 13 + 81 = 94 81 + -18x + x2 = 94 Factor a perfect square on the left side: (x + -9)(x + -9) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + -9) equal to 9.695359715 and -9.695359715.Subproblem 1
x + -9 = 9.695359715 Simplifying x + -9 = 9.695359715 Reorder the terms: -9 + x = 9.695359715 Solving -9 + x = 9.695359715 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 = 9.695359715 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.695359715 + 9 x = 9.695359715 + 9 Combine like terms: 9.695359715 + 9 = 18.695359715 x = 18.695359715 Simplifying x = 18.695359715Subproblem 2
x + -9 = -9.695359715 Simplifying x + -9 = -9.695359715 Reorder the terms: -9 + x = -9.695359715 Solving -9 + x = -9.695359715 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 = -9.695359715 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.695359715 + 9 x = -9.695359715 + 9 Combine like terms: -9.695359715 + 9 = -0.695359715 x = -0.695359715 Simplifying x = -0.695359715Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.695359715, -0.695359715}
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