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Simplifying x2 + -18x + -27 = 10 Reorder the terms: -27 + -18x + x2 = 10 Solving -27 + -18x + x2 = 10 Solving for variable 'x'. Reorder the terms: -27 + -10 + -18x + x2 = 10 + -10 Combine like terms: -27 + -10 = -37 -37 + -18x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -37 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -18x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + -18x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -18x + x2 = 0 + 37 -18x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 -18x + x2 = 37 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 = 37 + 81 Reorder the terms: 81 + -18x + x2 = 37 + 81 Combine like terms: 37 + 81 = 118 81 + -18x + x2 = 118 Factor a perfect square on the left side: (x + -9)(x + -9) = 118 Calculate the square root of the right side: 10.862780491 Break this problem into two subproblems by setting (x + -9) equal to 10.862780491 and -10.862780491.Subproblem 1
x + -9 = 10.862780491 Simplifying x + -9 = 10.862780491 Reorder the terms: -9 + x = 10.862780491 Solving -9 + x = 10.862780491 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 = 10.862780491 + 9 Combine like terms: -9 + 9 = 0 0 + x = 10.862780491 + 9 x = 10.862780491 + 9 Combine like terms: 10.862780491 + 9 = 19.862780491 x = 19.862780491 Simplifying x = 19.862780491Subproblem 2
x + -9 = -10.862780491 Simplifying x + -9 = -10.862780491 Reorder the terms: -9 + x = -10.862780491 Solving -9 + x = -10.862780491 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 = -10.862780491 + 9 Combine like terms: -9 + 9 = 0 0 + x = -10.862780491 + 9 x = -10.862780491 + 9 Combine like terms: -10.862780491 + 9 = -1.862780491 x = -1.862780491 Simplifying x = -1.862780491Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.862780491, -1.862780491}
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