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Simplifying x2 + -22x + -32 = 0 Reorder the terms: -32 + -22x + x2 = 0 Solving -32 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -22x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -22x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -22x + x2 = 0 + 32 -22x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -22x + x2 = 32 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 = 32 + 121 Reorder the terms: 121 + -22x + x2 = 32 + 121 Combine like terms: 32 + 121 = 153 121 + -22x + x2 = 153 Factor a perfect square on the left side: (x + -11)(x + -11) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (x + -11) equal to 12.369316877 and -12.369316877.Subproblem 1
x + -11 = 12.369316877 Simplifying x + -11 = 12.369316877 Reorder the terms: -11 + x = 12.369316877 Solving -11 + x = 12.369316877 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 = 12.369316877 + 11 Combine like terms: -11 + 11 = 0 0 + x = 12.369316877 + 11 x = 12.369316877 + 11 Combine like terms: 12.369316877 + 11 = 23.369316877 x = 23.369316877 Simplifying x = 23.369316877Subproblem 2
x + -11 = -12.369316877 Simplifying x + -11 = -12.369316877 Reorder the terms: -11 + x = -12.369316877 Solving -11 + x = -12.369316877 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 = -12.369316877 + 11 Combine like terms: -11 + 11 = 0 0 + x = -12.369316877 + 11 x = -12.369316877 + 11 Combine like terms: -12.369316877 + 11 = -1.369316877 x = -1.369316877 Simplifying x = -1.369316877Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.369316877, -1.369316877}
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