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Simplifying 6x2 + -132x + 121 = 0 Reorder the terms: 121 + -132x + 6x2 = 0 Solving 121 + -132x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 20.16666667 + -22x + x2 = 0 Move the constant term to the right: Add '-20.16666667' to each side of the equation. 20.16666667 + -22x + -20.16666667 + x2 = 0 + -20.16666667 Reorder the terms: 20.16666667 + -20.16666667 + -22x + x2 = 0 + -20.16666667 Combine like terms: 20.16666667 + -20.16666667 = 0.00000000 0.00000000 + -22x + x2 = 0 + -20.16666667 -22x + x2 = 0 + -20.16666667 Combine like terms: 0 + -20.16666667 = -20.16666667 -22x + x2 = -20.16666667 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 = -20.16666667 + 121 Reorder the terms: 121 + -22x + x2 = -20.16666667 + 121 Combine like terms: -20.16666667 + 121 = 100.83333333 121 + -22x + x2 = 100.83333333 Factor a perfect square on the left side: (x + -11)(x + -11) = 100.83333333 Calculate the square root of the right side: 10.041580221 Break this problem into two subproblems by setting (x + -11) equal to 10.041580221 and -10.041580221.Subproblem 1
x + -11 = 10.041580221 Simplifying x + -11 = 10.041580221 Reorder the terms: -11 + x = 10.041580221 Solving -11 + x = 10.041580221 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 = 10.041580221 + 11 Combine like terms: -11 + 11 = 0 0 + x = 10.041580221 + 11 x = 10.041580221 + 11 Combine like terms: 10.041580221 + 11 = 21.041580221 x = 21.041580221 Simplifying x = 21.041580221Subproblem 2
x + -11 = -10.041580221 Simplifying x + -11 = -10.041580221 Reorder the terms: -11 + x = -10.041580221 Solving -11 + x = -10.041580221 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 = -10.041580221 + 11 Combine like terms: -11 + 11 = 0 0 + x = -10.041580221 + 11 x = -10.041580221 + 11 Combine like terms: -10.041580221 + 11 = 0.958419779 x = 0.958419779 Simplifying x = 0.958419779Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.041580221, 0.958419779}
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