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Simplifying x2 + -18x + -99 = 0 Reorder the terms: -99 + -18x + x2 = 0 Solving -99 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -18x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -18x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -18x + x2 = 0 + 99 -18x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -18x + x2 = 99 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 = 99 + 81 Reorder the terms: 81 + -18x + x2 = 99 + 81 Combine like terms: 99 + 81 = 180 81 + -18x + x2 = 180 Factor a perfect square on the left side: (x + -9)(x + -9) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + -9) equal to 13.416407865 and -13.416407865.Subproblem 1
x + -9 = 13.416407865 Simplifying x + -9 = 13.416407865 Reorder the terms: -9 + x = 13.416407865 Solving -9 + x = 13.416407865 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 = 13.416407865 + 9 Combine like terms: -9 + 9 = 0 0 + x = 13.416407865 + 9 x = 13.416407865 + 9 Combine like terms: 13.416407865 + 9 = 22.416407865 x = 22.416407865 Simplifying x = 22.416407865Subproblem 2
x + -9 = -13.416407865 Simplifying x + -9 = -13.416407865 Reorder the terms: -9 + x = -13.416407865 Solving -9 + x = -13.416407865 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 = -13.416407865 + 9 Combine like terms: -9 + 9 = 0 0 + x = -13.416407865 + 9 x = -13.416407865 + 9 Combine like terms: -13.416407865 + 9 = -4.416407865 x = -4.416407865 Simplifying x = -4.416407865Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.416407865, -4.416407865}
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