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Simplifying 3x2 = -10x + -6 Reorder the terms: 3x2 = -6 + -10x Solving 3x2 = -6 + -10x Solving for variable 'x'. Reorder the terms: 6 + 10x + 3x2 = -6 + -10x + 6 + 10x Reorder the terms: 6 + 10x + 3x2 = -6 + 6 + -10x + 10x Combine like terms: -6 + 6 = 0 6 + 10x + 3x2 = 0 + -10x + 10x 6 + 10x + 3x2 = -10x + 10x Combine like terms: -10x + 10x = 0 6 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.333333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3.333333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.333333333x + x2 = 0 + -2 3.333333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.333333333x + x2 = -2 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = -2 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = -2 + 2.777777779 Combine like terms: -2 + 2.777777779 = 0.777777779 2.777777779 + 3.333333333x + x2 = 0.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 0.777777779 Calculate the square root of the right side: 0.881917104 Break this problem into two subproblems by setting (x + 1.666666667) equal to 0.881917104 and -0.881917104.Subproblem 1
x + 1.666666667 = 0.881917104 Simplifying x + 1.666666667 = 0.881917104 Reorder the terms: 1.666666667 + x = 0.881917104 Solving 1.666666667 + x = 0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 0.881917104 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 0.881917104 + -1.666666667 x = 0.881917104 + -1.666666667 Combine like terms: 0.881917104 + -1.666666667 = -0.784749563 x = -0.784749563 Simplifying x = -0.784749563Subproblem 2
x + 1.666666667 = -0.881917104 Simplifying x + 1.666666667 = -0.881917104 Reorder the terms: 1.666666667 + x = -0.881917104 Solving 1.666666667 + x = -0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -0.881917104 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -0.881917104 + -1.666666667 x = -0.881917104 + -1.666666667 Combine like terms: -0.881917104 + -1.666666667 = -2.548583771 x = -2.548583771 Simplifying x = -2.548583771Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.784749563, -2.548583771}
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