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Simplifying 6x2 + -22x + 20 = 323 Reorder the terms: 20 + -22x + 6x2 = 323 Solving 20 + -22x + 6x2 = 323 Solving for variable 'x'. Reorder the terms: 20 + -323 + -22x + 6x2 = 323 + -323 Combine like terms: 20 + -323 = -303 -303 + -22x + 6x2 = 323 + -323 Combine like terms: 323 + -323 = 0 -303 + -22x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -50.5 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '50.5' to each side of the equation. -50.5 + -3.666666667x + 50.5 + x2 = 0 + 50.5 Reorder the terms: -50.5 + 50.5 + -3.666666667x + x2 = 0 + 50.5 Combine like terms: -50.5 + 50.5 = 0.0 0.0 + -3.666666667x + x2 = 0 + 50.5 -3.666666667x + x2 = 0 + 50.5 Combine like terms: 0 + 50.5 = 50.5 -3.666666667x + x2 = 50.5 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 50.5 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 50.5 + 3.361111114 Combine like terms: 50.5 + 3.361111114 = 53.861111114 3.361111114 + -3.666666667x + x2 = 53.861111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 53.861111114 Calculate the square root of the right side: 7.339012952 Break this problem into two subproblems by setting (x + -1.833333334) equal to 7.339012952 and -7.339012952.Subproblem 1
x + -1.833333334 = 7.339012952 Simplifying x + -1.833333334 = 7.339012952 Reorder the terms: -1.833333334 + x = 7.339012952 Solving -1.833333334 + x = 7.339012952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 7.339012952 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 7.339012952 + 1.833333334 x = 7.339012952 + 1.833333334 Combine like terms: 7.339012952 + 1.833333334 = 9.172346286 x = 9.172346286 Simplifying x = 9.172346286Subproblem 2
x + -1.833333334 = -7.339012952 Simplifying x + -1.833333334 = -7.339012952 Reorder the terms: -1.833333334 + x = -7.339012952 Solving -1.833333334 + x = -7.339012952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -7.339012952 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -7.339012952 + 1.833333334 x = -7.339012952 + 1.833333334 Combine like terms: -7.339012952 + 1.833333334 = -5.505679618 x = -5.505679618 Simplifying x = -5.505679618Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.172346286, -5.505679618}
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