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Simplifying x2 + 22x = -16 Reorder the terms: 22x + x2 = -16 Solving 22x + x2 = -16 Solving for variable 'x'. Reorder the terms: 16 + 22x + x2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 22x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 22x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 22x + x2 = 0 + -16 22x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 22x + x2 = -16 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 = -16 + 121 Reorder the terms: 121 + 22x + x2 = -16 + 121 Combine like terms: -16 + 121 = 105 121 + 22x + x2 = 105 Factor a perfect square on the left side: (x + 11)(x + 11) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + 11) equal to 10.246950766 and -10.246950766.Subproblem 1
x + 11 = 10.246950766 Simplifying x + 11 = 10.246950766 Reorder the terms: 11 + x = 10.246950766 Solving 11 + x = 10.246950766 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 = 10.246950766 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.246950766 + -11 x = 10.246950766 + -11 Combine like terms: 10.246950766 + -11 = -0.753049234 x = -0.753049234 Simplifying x = -0.753049234Subproblem 2
x + 11 = -10.246950766 Simplifying x + 11 = -10.246950766 Reorder the terms: 11 + x = -10.246950766 Solving 11 + x = -10.246950766 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 = -10.246950766 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.246950766 + -11 x = -10.246950766 + -11 Combine like terms: -10.246950766 + -11 = -21.246950766 x = -21.246950766 Simplifying x = -21.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.753049234, -21.246950766}
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