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Simplifying (x2) + 6x + -115 = 0 x2 + 6x + -115 = 0 Reorder the terms: -115 + 6x + x2 = 0 Solving -115 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '115' to each side of the equation. -115 + 6x + 115 + x2 = 0 + 115 Reorder the terms: -115 + 115 + 6x + x2 = 0 + 115 Combine like terms: -115 + 115 = 0 0 + 6x + x2 = 0 + 115 6x + x2 = 0 + 115 Combine like terms: 0 + 115 = 115 6x + x2 = 115 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 = 115 + 9 Reorder the terms: 9 + 6x + x2 = 115 + 9 Combine like terms: 115 + 9 = 124 9 + 6x + x2 = 124 Factor a perfect square on the left side: (x + 3)(x + 3) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (x + 3) equal to 11.135528726 and -11.135528726.Subproblem 1
x + 3 = 11.135528726 Simplifying x + 3 = 11.135528726 Reorder the terms: 3 + x = 11.135528726 Solving 3 + x = 11.135528726 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 = 11.135528726 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.135528726 + -3 x = 11.135528726 + -3 Combine like terms: 11.135528726 + -3 = 8.135528726 x = 8.135528726 Simplifying x = 8.135528726Subproblem 2
x + 3 = -11.135528726 Simplifying x + 3 = -11.135528726 Reorder the terms: 3 + x = -11.135528726 Solving 3 + x = -11.135528726 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 = -11.135528726 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.135528726 + -3 x = -11.135528726 + -3 Combine like terms: -11.135528726 + -3 = -14.135528726 x = -14.135528726 Simplifying x = -14.135528726Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.135528726, -14.135528726}
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