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Simplifying x2 + 12x + -26 = 0 Reorder the terms: -26 + 12x + x2 = 0 Solving -26 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 12x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 12x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 12x + x2 = 0 + 26 12x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 12x + x2 = 26 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 = 26 + 36 Reorder the terms: 36 + 12x + x2 = 26 + 36 Combine like terms: 26 + 36 = 62 36 + 12x + x2 = 62 Factor a perfect square on the left side: (x + 6)(x + 6) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x + 6) equal to 7.874007874 and -7.874007874.Subproblem 1
x + 6 = 7.874007874 Simplifying x + 6 = 7.874007874 Reorder the terms: 6 + x = 7.874007874 Solving 6 + x = 7.874007874 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 = 7.874007874 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.874007874 + -6 x = 7.874007874 + -6 Combine like terms: 7.874007874 + -6 = 1.874007874 x = 1.874007874 Simplifying x = 1.874007874Subproblem 2
x + 6 = -7.874007874 Simplifying x + 6 = -7.874007874 Reorder the terms: 6 + x = -7.874007874 Solving 6 + x = -7.874007874 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 = -7.874007874 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.874007874 + -6 x = -7.874007874 + -6 Combine like terms: -7.874007874 + -6 = -13.874007874 x = -13.874007874 Simplifying x = -13.874007874Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.874007874, -13.874007874}
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