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Simplifying x2 + 10x + -18 = 180 Reorder the terms: -18 + 10x + x2 = 180 Solving -18 + 10x + x2 = 180 Solving for variable 'x'. Reorder the terms: -18 + -180 + 10x + x2 = 180 + -180 Combine like terms: -18 + -180 = -198 -198 + 10x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -198 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '198' to each side of the equation. -198 + 10x + 198 + x2 = 0 + 198 Reorder the terms: -198 + 198 + 10x + x2 = 0 + 198 Combine like terms: -198 + 198 = 0 0 + 10x + x2 = 0 + 198 10x + x2 = 0 + 198 Combine like terms: 0 + 198 = 198 10x + x2 = 198 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 198 + 25 Reorder the terms: 25 + 10x + x2 = 198 + 25 Combine like terms: 198 + 25 = 223 25 + 10x + x2 = 223 Factor a perfect square on the left side: (x + 5)(x + 5) = 223 Calculate the square root of the right side: 14.933184523 Break this problem into two subproblems by setting (x + 5) equal to 14.933184523 and -14.933184523.Subproblem 1
x + 5 = 14.933184523 Simplifying x + 5 = 14.933184523 Reorder the terms: 5 + x = 14.933184523 Solving 5 + x = 14.933184523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 14.933184523 + -5 Combine like terms: 5 + -5 = 0 0 + x = 14.933184523 + -5 x = 14.933184523 + -5 Combine like terms: 14.933184523 + -5 = 9.933184523 x = 9.933184523 Simplifying x = 9.933184523Subproblem 2
x + 5 = -14.933184523 Simplifying x + 5 = -14.933184523 Reorder the terms: 5 + x = -14.933184523 Solving 5 + x = -14.933184523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -14.933184523 + -5 Combine like terms: 5 + -5 = 0 0 + x = -14.933184523 + -5 x = -14.933184523 + -5 Combine like terms: -14.933184523 + -5 = -19.933184523 x = -19.933184523 Simplifying x = -19.933184523Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.933184523, -19.933184523}
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