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Simplifying x2 + 13x + 22 = x Reorder the terms: 22 + 13x + x2 = x Solving 22 + 13x + x2 = x Solving for variable 'x'. Reorder the terms: 22 + 13x + -1x + x2 = x + -1x Combine like terms: 13x + -1x = 12x 22 + 12x + x2 = x + -1x Combine like terms: x + -1x = 0 22 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 12x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + 12x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 12x + x2 = 0 + -22 12x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 12x + x2 = -22 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 = -22 + 36 Reorder the terms: 36 + 12x + x2 = -22 + 36 Combine like terms: -22 + 36 = 14 36 + 12x + x2 = 14 Factor a perfect square on the left side: (x + 6)(x + 6) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 6) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 6 = 3.741657387 Simplifying x + 6 = 3.741657387 Reorder the terms: 6 + x = 3.741657387 Solving 6 + x = 3.741657387 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 = 3.741657387 + -6 Combine like terms: 6 + -6 = 0 0 + x = 3.741657387 + -6 x = 3.741657387 + -6 Combine like terms: 3.741657387 + -6 = -2.258342613 x = -2.258342613 Simplifying x = -2.258342613Subproblem 2
x + 6 = -3.741657387 Simplifying x + 6 = -3.741657387 Reorder the terms: 6 + x = -3.741657387 Solving 6 + x = -3.741657387 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 = -3.741657387 + -6 Combine like terms: 6 + -6 = 0 0 + x = -3.741657387 + -6 x = -3.741657387 + -6 Combine like terms: -3.741657387 + -6 = -9.741657387 x = -9.741657387 Simplifying x = -9.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.258342613, -9.741657387}
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