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Simplifying 6x2 + 22x = -17 Reorder the terms: 22x + 6x2 = -17 Solving 22x + 6x2 = -17 Solving for variable 'x'. Reorder the terms: 17 + 22x + 6x2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + 22x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.833333333 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '-2.833333333' to each side of the equation. 2.833333333 + 3.666666667x + -2.833333333 + x2 = 0 + -2.833333333 Reorder the terms: 2.833333333 + -2.833333333 + 3.666666667x + x2 = 0 + -2.833333333 Combine like terms: 2.833333333 + -2.833333333 = 0.000000000 0.000000000 + 3.666666667x + x2 = 0 + -2.833333333 3.666666667x + x2 = 0 + -2.833333333 Combine like terms: 0 + -2.833333333 = -2.833333333 3.666666667x + x2 = -2.833333333 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 = -2.833333333 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = -2.833333333 + 3.361111114 Combine like terms: -2.833333333 + 3.361111114 = 0.527777781 3.361111114 + 3.666666667x + x2 = 0.527777781 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 0.527777781 Calculate the square root of the right side: 0.726483159 Break this problem into two subproblems by setting (x + 1.833333334) equal to 0.726483159 and -0.726483159.Subproblem 1
x + 1.833333334 = 0.726483159 Simplifying x + 1.833333334 = 0.726483159 Reorder the terms: 1.833333334 + x = 0.726483159 Solving 1.833333334 + x = 0.726483159 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 = 0.726483159 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 0.726483159 + -1.833333334 x = 0.726483159 + -1.833333334 Combine like terms: 0.726483159 + -1.833333334 = -1.106850175 x = -1.106850175 Simplifying x = -1.106850175Subproblem 2
x + 1.833333334 = -0.726483159 Simplifying x + 1.833333334 = -0.726483159 Reorder the terms: 1.833333334 + x = -0.726483159 Solving 1.833333334 + x = -0.726483159 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 = -0.726483159 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -0.726483159 + -1.833333334 x = -0.726483159 + -1.833333334 Combine like terms: -0.726483159 + -1.833333334 = -2.559816493 x = -2.559816493 Simplifying x = -2.559816493Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.106850175, -2.559816493}
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