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Simplifying 0 = x2 + -22x + 12 Reorder the terms: 0 = 12 + -22x + x2 Solving 0 = 12 + -22x + x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + 22x + -1x2 = 12 + -22x + x2 + -12 + 22x + -1x2 Reorder the terms: -12 + 22x + -1x2 = 12 + -12 + -22x + 22x + x2 + -1x2 Combine like terms: 12 + -12 = 0 -12 + 22x + -1x2 = 0 + -22x + 22x + x2 + -1x2 -12 + 22x + -1x2 = -22x + 22x + x2 + -1x2 Combine like terms: -22x + 22x = 0 -12 + 22x + -1x2 = 0 + x2 + -1x2 -12 + 22x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + 22x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -22x + x2 = 0 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 = 21.440306509 x = 21.440306509 Simplifying x = 21.440306509Subproblem 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 = 0.559693491 x = 0.559693491 Simplifying x = 0.559693491Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.440306509, 0.559693491}
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