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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 = 133 121 + -22x + x2 = 133 Factor a perfect square on the left side: (x + -11)(x + -11) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (x + -11) equal to 11.532562595 and -11.532562595.Subproblem 1
x + -11 = 11.532562595 Simplifying x + -11 = 11.532562595 Reorder the terms: -11 + x = 11.532562595 Solving -11 + x = 11.532562595 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 = 11.532562595 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.532562595 + 11 x = 11.532562595 + 11 Combine like terms: 11.532562595 + 11 = 22.532562595 x = 22.532562595 Simplifying x = 22.532562595Subproblem 2
x + -11 = -11.532562595 Simplifying x + -11 = -11.532562595 Reorder the terms: -11 + x = -11.532562595 Solving -11 + x = -11.532562595 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 = -11.532562595 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.532562595 + 11 x = -11.532562595 + 11 Combine like terms: -11.532562595 + 11 = -0.532562595 x = -0.532562595 Simplifying x = -0.532562595Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.532562595, -0.532562595}
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