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Simplifying 1.5x2 = 5.5x + -2.2 Reorder the terms: 1.5x2 = -2.2 + 5.5x Solving 1.5x2 = -2.2 + 5.5x Solving for variable 'x'. Reorder the terms: 2.2 + -5.5x + 1.5x2 = -2.2 + 5.5x + 2.2 + -5.5x Reorder the terms: 2.2 + -5.5x + 1.5x2 = -2.2 + 2.2 + 5.5x + -5.5x Combine like terms: -2.2 + 2.2 = 0.0 2.2 + -5.5x + 1.5x2 = 0.0 + 5.5x + -5.5x 2.2 + -5.5x + 1.5x2 = 5.5x + -5.5x Combine like terms: 5.5x + -5.5x = 0.0 2.2 + -5.5x + 1.5x2 = 0.0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 1.466666667 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '-1.466666667' to each side of the equation. 1.466666667 + -3.666666667x + -1.466666667 + x2 = 0 + -1.466666667 Reorder the terms: 1.466666667 + -1.466666667 + -3.666666667x + x2 = 0 + -1.466666667 Combine like terms: 1.466666667 + -1.466666667 = 0.000000000 0.000000000 + -3.666666667x + x2 = 0 + -1.466666667 -3.666666667x + x2 = 0 + -1.466666667 Combine like terms: 0 + -1.466666667 = -1.466666667 -3.666666667x + x2 = -1.466666667 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 = -1.466666667 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = -1.466666667 + 3.361111114 Combine like terms: -1.466666667 + 3.361111114 = 1.894444447 3.361111114 + -3.666666667x + x2 = 1.894444447 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 1.894444447 Calculate the square root of the right side: 1.376388189 Break this problem into two subproblems by setting (x + -1.833333334) equal to 1.376388189 and -1.376388189.Subproblem 1
x + -1.833333334 = 1.376388189 Simplifying x + -1.833333334 = 1.376388189 Reorder the terms: -1.833333334 + x = 1.376388189 Solving -1.833333334 + x = 1.376388189 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 = 1.376388189 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 1.376388189 + 1.833333334 x = 1.376388189 + 1.833333334 Combine like terms: 1.376388189 + 1.833333334 = 3.209721523 x = 3.209721523 Simplifying x = 3.209721523Subproblem 2
x + -1.833333334 = -1.376388189 Simplifying x + -1.833333334 = -1.376388189 Reorder the terms: -1.833333334 + x = -1.376388189 Solving -1.833333334 + x = -1.376388189 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 = -1.376388189 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -1.376388189 + 1.833333334 x = -1.376388189 + 1.833333334 Combine like terms: -1.376388189 + 1.833333334 = 0.456945145 x = 0.456945145 Simplifying x = 0.456945145Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.209721523, 0.456945145}
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