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Simplifying x2 + 22x + -22 = 0 Reorder the terms: -22 + 22x + x2 = 0 Solving -22 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 22x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 22x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 22x + x2 = 0 + 22 22x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 22x + x2 = 22 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 = 22 + 121 Reorder the terms: 121 + 22x + x2 = 22 + 121 Combine like terms: 22 + 121 = 143 121 + 22x + x2 = 143 Factor a perfect square on the left side: (x + 11)(x + 11) = 143 Calculate the square root of the right side: 11.958260743 Break this problem into two subproblems by setting (x + 11) equal to 11.958260743 and -11.958260743.Subproblem 1
x + 11 = 11.958260743 Simplifying x + 11 = 11.958260743 Reorder the terms: 11 + x = 11.958260743 Solving 11 + x = 11.958260743 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 = 11.958260743 + -11 Combine like terms: 11 + -11 = 0 0 + x = 11.958260743 + -11 x = 11.958260743 + -11 Combine like terms: 11.958260743 + -11 = 0.958260743 x = 0.958260743 Simplifying x = 0.958260743Subproblem 2
x + 11 = -11.958260743 Simplifying x + 11 = -11.958260743 Reorder the terms: 11 + x = -11.958260743 Solving 11 + x = -11.958260743 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 = -11.958260743 + -11 Combine like terms: 11 + -11 = 0 0 + x = -11.958260743 + -11 x = -11.958260743 + -11 Combine like terms: -11.958260743 + -11 = -22.958260743 x = -22.958260743 Simplifying x = -22.958260743Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.958260743, -22.958260743}
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