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Simplifying x2 + -12x + 22 = 0 Reorder the terms: 22 + -12x + x2 = 0 Solving 22 + -12x + x2 = 0 Solving for variable 'x'. 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 = 9.741657387 x = 9.741657387 Simplifying x = 9.741657387Subproblem 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 = 2.258342613 x = 2.258342613 Simplifying x = 2.258342613Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.741657387, 2.258342613}
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