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Simplifying 3x2 + -11x + 6 = 25 Reorder the terms: 6 + -11x + 3x2 = 25 Solving 6 + -11x + 3x2 = 25 Solving for variable 'x'. Reorder the terms: 6 + -25 + -11x + 3x2 = 25 + -25 Combine like terms: 6 + -25 = -19 -19 + -11x + 3x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -19 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.333333333 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + -3.666666667x + 6.333333333 + x2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + -3.666666667x + x2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + -3.666666667x + x2 = 0 + 6.333333333 -3.666666667x + x2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 -3.666666667x + x2 = 6.333333333 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 = 6.333333333 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 6.333333333 + 3.361111114 Combine like terms: 6.333333333 + 3.361111114 = 9.694444447 3.361111114 + -3.666666667x + x2 = 9.694444447 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 9.694444447 Calculate the square root of the right side: 3.113590282 Break this problem into two subproblems by setting (x + -1.833333334) equal to 3.113590282 and -3.113590282.Subproblem 1
x + -1.833333334 = 3.113590282 Simplifying x + -1.833333334 = 3.113590282 Reorder the terms: -1.833333334 + x = 3.113590282 Solving -1.833333334 + x = 3.113590282 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 = 3.113590282 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 3.113590282 + 1.833333334 x = 3.113590282 + 1.833333334 Combine like terms: 3.113590282 + 1.833333334 = 4.946923616 x = 4.946923616 Simplifying x = 4.946923616Subproblem 2
x + -1.833333334 = -3.113590282 Simplifying x + -1.833333334 = -3.113590282 Reorder the terms: -1.833333334 + x = -3.113590282 Solving -1.833333334 + x = -3.113590282 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 = -3.113590282 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -3.113590282 + 1.833333334 x = -3.113590282 + 1.833333334 Combine like terms: -3.113590282 + 1.833333334 = -1.280256948 x = -1.280256948 Simplifying x = -1.280256948Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.946923616, -1.280256948}
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