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Simplifying x2 + -18x + 66 = 0 Reorder the terms: 66 + -18x + x2 = 0 Solving 66 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-66' to each side of the equation. 66 + -18x + -66 + x2 = 0 + -66 Reorder the terms: 66 + -66 + -18x + x2 = 0 + -66 Combine like terms: 66 + -66 = 0 0 + -18x + x2 = 0 + -66 -18x + x2 = 0 + -66 Combine like terms: 0 + -66 = -66 -18x + x2 = -66 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 = -66 + 81 Reorder the terms: 81 + -18x + x2 = -66 + 81 Combine like terms: -66 + 81 = 15 81 + -18x + x2 = 15 Factor a perfect square on the left side: (x + -9)(x + -9) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -9) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -9 = 3.872983346 Simplifying x + -9 = 3.872983346 Reorder the terms: -9 + x = 3.872983346 Solving -9 + x = 3.872983346 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 = 3.872983346 + 9 Combine like terms: -9 + 9 = 0 0 + x = 3.872983346 + 9 x = 3.872983346 + 9 Combine like terms: 3.872983346 + 9 = 12.872983346 x = 12.872983346 Simplifying x = 12.872983346Subproblem 2
x + -9 = -3.872983346 Simplifying x + -9 = -3.872983346 Reorder the terms: -9 + x = -3.872983346 Solving -9 + x = -3.872983346 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 = -3.872983346 + 9 Combine like terms: -9 + 9 = 0 0 + x = -3.872983346 + 9 x = -3.872983346 + 9 Combine like terms: -3.872983346 + 9 = 5.127016654 x = 5.127016654 Simplifying x = 5.127016654Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.872983346, 5.127016654}
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