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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 = 6.194444447 3.361111114 + 3.666666667x + x2 = 6.194444447 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 6.194444447 Calculate the square root of the right side: 2.488864088 Break this problem into two subproblems by setting (x + 1.833333334) equal to 2.488864088 and -2.488864088.Subproblem 1
x + 1.833333334 = 2.488864088 Simplifying x + 1.833333334 = 2.488864088 Reorder the terms: 1.833333334 + x = 2.488864088 Solving 1.833333334 + x = 2.488864088 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 = 2.488864088 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 2.488864088 + -1.833333334 x = 2.488864088 + -1.833333334 Combine like terms: 2.488864088 + -1.833333334 = 0.655530754 x = 0.655530754 Simplifying x = 0.655530754Subproblem 2
x + 1.833333334 = -2.488864088 Simplifying x + 1.833333334 = -2.488864088 Reorder the terms: 1.833333334 + x = -2.488864088 Solving 1.833333334 + x = -2.488864088 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 = -2.488864088 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -2.488864088 + -1.833333334 x = -2.488864088 + -1.833333334 Combine like terms: -2.488864088 + -1.833333334 = -4.322197422 x = -4.322197422 Simplifying x = -4.322197422Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.655530754, -4.322197422}
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