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Simplifying x2 + 18x + -100 = 0 Reorder the terms: -100 + 18x + x2 = 0 Solving -100 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 18x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 18x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 18x + x2 = 0 + 100 18x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 18x + x2 = 100 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 = 100 + 81 Reorder the terms: 81 + 18x + x2 = 100 + 81 Combine like terms: 100 + 81 = 181 81 + 18x + x2 = 181 Factor a perfect square on the left side: (x + 9)(x + 9) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (x + 9) equal to 13.453624047 and -13.453624047.Subproblem 1
x + 9 = 13.453624047 Simplifying x + 9 = 13.453624047 Reorder the terms: 9 + x = 13.453624047 Solving 9 + x = 13.453624047 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 = 13.453624047 + -9 Combine like terms: 9 + -9 = 0 0 + x = 13.453624047 + -9 x = 13.453624047 + -9 Combine like terms: 13.453624047 + -9 = 4.453624047 x = 4.453624047 Simplifying x = 4.453624047Subproblem 2
x + 9 = -13.453624047 Simplifying x + 9 = -13.453624047 Reorder the terms: 9 + x = -13.453624047 Solving 9 + x = -13.453624047 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 = -13.453624047 + -9 Combine like terms: 9 + -9 = 0 0 + x = -13.453624047 + -9 x = -13.453624047 + -9 Combine like terms: -13.453624047 + -9 = -22.453624047 x = -22.453624047 Simplifying x = -22.453624047Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.453624047, -22.453624047}
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