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Simplifying x2 + -24x + 22 = 0 Reorder the terms: 22 + -24x + x2 = 0 Solving 22 + -24x + 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 + -24x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -24x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -24x + x2 = 0 + -22 -24x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -24x + x2 = -22 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -22 + 144 Reorder the terms: 144 + -24x + x2 = -22 + 144 Combine like terms: -22 + 144 = 122 144 + -24x + x2 = 122 Factor a perfect square on the left side: (x + -12)(x + -12) = 122 Calculate the square root of the right side: 11.045361017 Break this problem into two subproblems by setting (x + -12) equal to 11.045361017 and -11.045361017.Subproblem 1
x + -12 = 11.045361017 Simplifying x + -12 = 11.045361017 Reorder the terms: -12 + x = 11.045361017 Solving -12 + x = 11.045361017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 11.045361017 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.045361017 + 12 x = 11.045361017 + 12 Combine like terms: 11.045361017 + 12 = 23.045361017 x = 23.045361017 Simplifying x = 23.045361017Subproblem 2
x + -12 = -11.045361017 Simplifying x + -12 = -11.045361017 Reorder the terms: -12 + x = -11.045361017 Solving -12 + x = -11.045361017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -11.045361017 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.045361017 + 12 x = -11.045361017 + 12 Combine like terms: -11.045361017 + 12 = 0.954638983 x = 0.954638983 Simplifying x = 0.954638983Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.045361017, 0.954638983}
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