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Simplifying x2 + 22x + -125 = 2 Reorder the terms: -125 + 22x + x2 = 2 Solving -125 + 22x + x2 = 2 Solving for variable 'x'. Reorder the terms: -125 + -2 + 22x + x2 = 2 + -2 Combine like terms: -125 + -2 = -127 -127 + 22x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -127 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '127' to each side of the equation. -127 + 22x + 127 + x2 = 0 + 127 Reorder the terms: -127 + 127 + 22x + x2 = 0 + 127 Combine like terms: -127 + 127 = 0 0 + 22x + x2 = 0 + 127 22x + x2 = 0 + 127 Combine like terms: 0 + 127 = 127 22x + x2 = 127 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 = 127 + 121 Reorder the terms: 121 + 22x + x2 = 127 + 121 Combine like terms: 127 + 121 = 248 121 + 22x + x2 = 248 Factor a perfect square on the left side: (x + 11)(x + 11) = 248 Calculate the square root of the right side: 15.748015748 Break this problem into two subproblems by setting (x + 11) equal to 15.748015748 and -15.748015748.Subproblem 1
x + 11 = 15.748015748 Simplifying x + 11 = 15.748015748 Reorder the terms: 11 + x = 15.748015748 Solving 11 + x = 15.748015748 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 = 15.748015748 + -11 Combine like terms: 11 + -11 = 0 0 + x = 15.748015748 + -11 x = 15.748015748 + -11 Combine like terms: 15.748015748 + -11 = 4.748015748 x = 4.748015748 Simplifying x = 4.748015748Subproblem 2
x + 11 = -15.748015748 Simplifying x + 11 = -15.748015748 Reorder the terms: 11 + x = -15.748015748 Solving 11 + x = -15.748015748 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 = -15.748015748 + -11 Combine like terms: 11 + -11 = 0 0 + x = -15.748015748 + -11 x = -15.748015748 + -11 Combine like terms: -15.748015748 + -11 = -26.748015748 x = -26.748015748 Simplifying x = -26.748015748Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.748015748, -26.748015748}
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