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Simplifying x2 + -22x + -34 = 0 Reorder the terms: -34 + -22x + x2 = 0 Solving -34 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -22x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -22x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -22x + x2 = 0 + 34 -22x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -22x + x2 = 34 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 = 34 + 121 Reorder the terms: 121 + -22x + x2 = 34 + 121 Combine like terms: 34 + 121 = 155 121 + -22x + x2 = 155 Factor a perfect square on the left side: (x + -11)(x + -11) = 155 Calculate the square root of the right side: 12.449899598 Break this problem into two subproblems by setting (x + -11) equal to 12.449899598 and -12.449899598.Subproblem 1
x + -11 = 12.449899598 Simplifying x + -11 = 12.449899598 Reorder the terms: -11 + x = 12.449899598 Solving -11 + x = 12.449899598 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 = 12.449899598 + 11 Combine like terms: -11 + 11 = 0 0 + x = 12.449899598 + 11 x = 12.449899598 + 11 Combine like terms: 12.449899598 + 11 = 23.449899598 x = 23.449899598 Simplifying x = 23.449899598Subproblem 2
x + -11 = -12.449899598 Simplifying x + -11 = -12.449899598 Reorder the terms: -11 + x = -12.449899598 Solving -11 + x = -12.449899598 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 = -12.449899598 + 11 Combine like terms: -11 + 11 = 0 0 + x = -12.449899598 + 11 x = -12.449899598 + 11 Combine like terms: -12.449899598 + 11 = -1.449899598 x = -1.449899598 Simplifying x = -1.449899598Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.449899598, -1.449899598}
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