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Simplifying x2 + 12x = 138 Reorder the terms: 12x + x2 = 138 Solving 12x + x2 = 138 Solving for variable 'x'. Reorder the terms: -138 + 12x + x2 = 138 + -138 Combine like terms: 138 + -138 = 0 -138 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '138' to each side of the equation. -138 + 12x + 138 + x2 = 0 + 138 Reorder the terms: -138 + 138 + 12x + x2 = 0 + 138 Combine like terms: -138 + 138 = 0 0 + 12x + x2 = 0 + 138 12x + x2 = 0 + 138 Combine like terms: 0 + 138 = 138 12x + x2 = 138 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 138 + 36 Reorder the terms: 36 + 12x + x2 = 138 + 36 Combine like terms: 138 + 36 = 174 36 + 12x + x2 = 174 Factor a perfect square on the left side: (x + 6)(x + 6) = 174 Calculate the square root of the right side: 13.190905958 Break this problem into two subproblems by setting (x + 6) equal to 13.190905958 and -13.190905958.Subproblem 1
x + 6 = 13.190905958 Simplifying x + 6 = 13.190905958 Reorder the terms: 6 + x = 13.190905958 Solving 6 + x = 13.190905958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 13.190905958 + -6 Combine like terms: 6 + -6 = 0 0 + x = 13.190905958 + -6 x = 13.190905958 + -6 Combine like terms: 13.190905958 + -6 = 7.190905958 x = 7.190905958 Simplifying x = 7.190905958Subproblem 2
x + 6 = -13.190905958 Simplifying x + 6 = -13.190905958 Reorder the terms: 6 + x = -13.190905958 Solving 6 + x = -13.190905958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -13.190905958 + -6 Combine like terms: 6 + -6 = 0 0 + x = -13.190905958 + -6 x = -13.190905958 + -6 Combine like terms: -13.190905958 + -6 = -19.190905958 x = -19.190905958 Simplifying x = -19.190905958Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.190905958, -19.190905958}
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