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Simplifying 3x2 + -10x + -13 = x + -6 Reorder the terms: -13 + -10x + 3x2 = x + -6 Reorder the terms: -13 + -10x + 3x2 = -6 + x Solving -13 + -10x + 3x2 = -6 + x Solving for variable 'x'. Reorder the terms: -13 + 6 + -10x + -1x + 3x2 = -6 + x + 6 + -1x Combine like terms: -13 + 6 = -7 -7 + -10x + -1x + 3x2 = -6 + x + 6 + -1x Combine like terms: -10x + -1x = -11x -7 + -11x + 3x2 = -6 + x + 6 + -1x Reorder the terms: -7 + -11x + 3x2 = -6 + 6 + x + -1x Combine like terms: -6 + 6 = 0 -7 + -11x + 3x2 = 0 + x + -1x -7 + -11x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -7 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -3.666666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -3.666666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -3.666666667x + x2 = 0 + 2.333333333 -3.666666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -3.666666667x + x2 = 2.333333333 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 = 2.333333333 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 2.333333333 + 3.361111114 Combine like terms: 2.333333333 + 3.361111114 = 5.694444447 3.361111114 + -3.666666667x + x2 = 5.694444447 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 5.694444447 Calculate the square root of the right side: 2.386303511 Break this problem into two subproblems by setting (x + -1.833333334) equal to 2.386303511 and -2.386303511.Subproblem 1
x + -1.833333334 = 2.386303511 Simplifying x + -1.833333334 = 2.386303511 Reorder the terms: -1.833333334 + x = 2.386303511 Solving -1.833333334 + x = 2.386303511 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 = 2.386303511 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 2.386303511 + 1.833333334 x = 2.386303511 + 1.833333334 Combine like terms: 2.386303511 + 1.833333334 = 4.219636845 x = 4.219636845 Simplifying x = 4.219636845Subproblem 2
x + -1.833333334 = -2.386303511 Simplifying x + -1.833333334 = -2.386303511 Reorder the terms: -1.833333334 + x = -2.386303511 Solving -1.833333334 + x = -2.386303511 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 = -2.386303511 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -2.386303511 + 1.833333334 x = -2.386303511 + 1.833333334 Combine like terms: -2.386303511 + 1.833333334 = -0.552970177 x = -0.552970177 Simplifying x = -0.552970177Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.219636845, -0.552970177}
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