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Simplifying -4 + 22x + -1x2 = 0 Solving -4 + 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'. 4 + -22x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -22x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -22x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -22x + x2 = 0 + -4 -22x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -22x + x2 = -4 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 = -4 + 121 Reorder the terms: 121 + -22x + x2 = -4 + 121 Combine like terms: -4 + 121 = 117 121 + -22x + x2 = 117 Factor a perfect square on the left side: (x + -11)(x + -11) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + -11) equal to 10.816653826 and -10.816653826.Subproblem 1
x + -11 = 10.816653826 Simplifying x + -11 = 10.816653826 Reorder the terms: -11 + x = 10.816653826 Solving -11 + x = 10.816653826 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 = 10.816653826 + 11 Combine like terms: -11 + 11 = 0 0 + x = 10.816653826 + 11 x = 10.816653826 + 11 Combine like terms: 10.816653826 + 11 = 21.816653826 x = 21.816653826 Simplifying x = 21.816653826Subproblem 2
x + -11 = -10.816653826 Simplifying x + -11 = -10.816653826 Reorder the terms: -11 + x = -10.816653826 Solving -11 + x = -10.816653826 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 = -10.816653826 + 11 Combine like terms: -11 + 11 = 0 0 + x = -10.816653826 + 11 x = -10.816653826 + 11 Combine like terms: -10.816653826 + 11 = 0.183346174 x = 0.183346174 Simplifying x = 0.183346174Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.816653826, 0.183346174}
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