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Simplifying x2 + -6x + -138 = 0 Reorder the terms: -138 + -6x + x2 = 0 Solving -138 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '138' to each side of the equation. -138 + -6x + 138 + x2 = 0 + 138 Reorder the terms: -138 + 138 + -6x + x2 = 0 + 138 Combine like terms: -138 + 138 = 0 0 + -6x + x2 = 0 + 138 -6x + x2 = 0 + 138 Combine like terms: 0 + 138 = 138 -6x + x2 = 138 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 138 + 9 Reorder the terms: 9 + -6x + x2 = 138 + 9 Combine like terms: 138 + 9 = 147 9 + -6x + x2 = 147 Factor a perfect square on the left side: (x + -3)(x + -3) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (x + -3) equal to 12.124355653 and -12.124355653.Subproblem 1
x + -3 = 12.124355653 Simplifying x + -3 = 12.124355653 Reorder the terms: -3 + x = 12.124355653 Solving -3 + x = 12.124355653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 12.124355653 + 3 Combine like terms: -3 + 3 = 0 0 + x = 12.124355653 + 3 x = 12.124355653 + 3 Combine like terms: 12.124355653 + 3 = 15.124355653 x = 15.124355653 Simplifying x = 15.124355653Subproblem 2
x + -3 = -12.124355653 Simplifying x + -3 = -12.124355653 Reorder the terms: -3 + x = -12.124355653 Solving -3 + x = -12.124355653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -12.124355653 + 3 Combine like terms: -3 + 3 = 0 0 + x = -12.124355653 + 3 x = -12.124355653 + 3 Combine like terms: -12.124355653 + 3 = -9.124355653 x = -9.124355653 Simplifying x = -9.124355653Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.124355653, -9.124355653}
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