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Simplifying x2 + -22x + -120 = 0 Reorder the terms: -120 + -22x + x2 = 0 Solving -120 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + -22x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -22x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -22x + x2 = 0 + 120 -22x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -22x + x2 = 120 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 = 120 + 121 Reorder the terms: 121 + -22x + x2 = 120 + 121 Combine like terms: 120 + 121 = 241 121 + -22x + x2 = 241 Factor a perfect square on the left side: (x + -11)(x + -11) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (x + -11) equal to 15.524174696 and -15.524174696.Subproblem 1
x + -11 = 15.524174696 Simplifying x + -11 = 15.524174696 Reorder the terms: -11 + x = 15.524174696 Solving -11 + x = 15.524174696 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 = 15.524174696 + 11 Combine like terms: -11 + 11 = 0 0 + x = 15.524174696 + 11 x = 15.524174696 + 11 Combine like terms: 15.524174696 + 11 = 26.524174696 x = 26.524174696 Simplifying x = 26.524174696Subproblem 2
x + -11 = -15.524174696 Simplifying x + -11 = -15.524174696 Reorder the terms: -11 + x = -15.524174696 Solving -11 + x = -15.524174696 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 = -15.524174696 + 11 Combine like terms: -11 + 11 = 0 0 + x = -15.524174696 + 11 x = -15.524174696 + 11 Combine like terms: -15.524174696 + 11 = -4.524174696 x = -4.524174696 Simplifying x = -4.524174696Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.524174696, -4.524174696}
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