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Simplifying x2 + 12x + -91 = 2 Reorder the terms: -91 + 12x + x2 = 2 Solving -91 + 12x + x2 = 2 Solving for variable 'x'. Reorder the terms: -91 + -2 + 12x + x2 = 2 + -2 Combine like terms: -91 + -2 = -93 -93 + 12x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -93 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '93' to each side of the equation. -93 + 12x + 93 + x2 = 0 + 93 Reorder the terms: -93 + 93 + 12x + x2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + 12x + x2 = 0 + 93 12x + x2 = 0 + 93 Combine like terms: 0 + 93 = 93 12x + x2 = 93 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 = 93 + 36 Reorder the terms: 36 + 12x + x2 = 93 + 36 Combine like terms: 93 + 36 = 129 36 + 12x + x2 = 129 Factor a perfect square on the left side: (x + 6)(x + 6) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + 6) equal to 11.357816692 and -11.357816692.Subproblem 1
x + 6 = 11.357816692 Simplifying x + 6 = 11.357816692 Reorder the terms: 6 + x = 11.357816692 Solving 6 + x = 11.357816692 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 = 11.357816692 + -6 Combine like terms: 6 + -6 = 0 0 + x = 11.357816692 + -6 x = 11.357816692 + -6 Combine like terms: 11.357816692 + -6 = 5.357816692 x = 5.357816692 Simplifying x = 5.357816692Subproblem 2
x + 6 = -11.357816692 Simplifying x + 6 = -11.357816692 Reorder the terms: 6 + x = -11.357816692 Solving 6 + x = -11.357816692 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 = -11.357816692 + -6 Combine like terms: 6 + -6 = 0 0 + x = -11.357816692 + -6 x = -11.357816692 + -6 Combine like terms: -11.357816692 + -6 = -17.357816692 x = -17.357816692 Simplifying x = -17.357816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.357816692, -17.357816692}
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