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Simplifying x2 + 22x + 12 = 0 Reorder the terms: 12 + 22x + x2 = 0 Solving 12 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 22x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 22x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 22x + x2 = 0 + -12 22x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 22x + x2 = -12 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -12 + 121 Reorder the terms: 121 + 22x + x2 = -12 + 121 Combine like terms: -12 + 121 = 109 121 + 22x + x2 = 109 Factor a perfect square on the left side: (x + 11)(x + 11) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + 11) equal to 10.440306509 and -10.440306509.Subproblem 1
x + 11 = 10.440306509 Simplifying x + 11 = 10.440306509 Reorder the terms: 11 + x = 10.440306509 Solving 11 + x = 10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 10.440306509 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.440306509 + -11 x = 10.440306509 + -11 Combine like terms: 10.440306509 + -11 = -0.559693491 x = -0.559693491 Simplifying x = -0.559693491Subproblem 2
x + 11 = -10.440306509 Simplifying x + 11 = -10.440306509 Reorder the terms: 11 + x = -10.440306509 Solving 11 + x = -10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -10.440306509 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.440306509 + -11 x = -10.440306509 + -11 Combine like terms: -10.440306509 + -11 = -21.440306509 x = -21.440306509 Simplifying x = -21.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.559693491, -21.440306509}
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