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Simplifying x2 + -22x + -99 = 0 Reorder the terms: -99 + -22x + x2 = 0 Solving -99 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -22x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -22x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -22x + x2 = 0 + 99 -22x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -22x + x2 = 99 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 = 99 + 121 Reorder the terms: 121 + -22x + x2 = 99 + 121 Combine like terms: 99 + 121 = 220 121 + -22x + x2 = 220 Factor a perfect square on the left side: (x + -11)(x + -11) = 220 Calculate the square root of the right side: 14.832396974 Break this problem into two subproblems by setting (x + -11) equal to 14.832396974 and -14.832396974.Subproblem 1
x + -11 = 14.832396974 Simplifying x + -11 = 14.832396974 Reorder the terms: -11 + x = 14.832396974 Solving -11 + x = 14.832396974 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 = 14.832396974 + 11 Combine like terms: -11 + 11 = 0 0 + x = 14.832396974 + 11 x = 14.832396974 + 11 Combine like terms: 14.832396974 + 11 = 25.832396974 x = 25.832396974 Simplifying x = 25.832396974Subproblem 2
x + -11 = -14.832396974 Simplifying x + -11 = -14.832396974 Reorder the terms: -11 + x = -14.832396974 Solving -11 + x = -14.832396974 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 = -14.832396974 + 11 Combine like terms: -11 + 11 = 0 0 + x = -14.832396974 + 11 x = -14.832396974 + 11 Combine like terms: -14.832396974 + 11 = -3.832396974 x = -3.832396974 Simplifying x = -3.832396974Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.832396974, -3.832396974}
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