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Simplifying -1x2 + 22x + 13 = 0 Reorder the terms: 13 + 22x + -1x2 = 0 Solving 13 + 22x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + -22x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -22x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -22x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -22x + x2 = 0 + 13 -22x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -22x + x2 = 13 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 = 13 + 121 Reorder the terms: 121 + -22x + x2 = 13 + 121 Combine like terms: 13 + 121 = 134 121 + -22x + x2 = 134 Factor a perfect square on the left side: (x + -11)(x + -11) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (x + -11) equal to 11.575836903 and -11.575836903.Subproblem 1
x + -11 = 11.575836903 Simplifying x + -11 = 11.575836903 Reorder the terms: -11 + x = 11.575836903 Solving -11 + x = 11.575836903 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 = 11.575836903 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.575836903 + 11 x = 11.575836903 + 11 Combine like terms: 11.575836903 + 11 = 22.575836903 x = 22.575836903 Simplifying x = 22.575836903Subproblem 2
x + -11 = -11.575836903 Simplifying x + -11 = -11.575836903 Reorder the terms: -11 + x = -11.575836903 Solving -11 + x = -11.575836903 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 = -11.575836903 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.575836903 + 11 x = -11.575836903 + 11 Combine like terms: -11.575836903 + 11 = -0.575836903 x = -0.575836903 Simplifying x = -0.575836903Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.575836903, -0.575836903}
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