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Simplifying 3x6 + -10x3 + -3 = 0 Reorder the terms: -3 + -10x3 + 3x6 = 0 Solving -3 + -10x3 + 3x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -3.333333333x3 + x6 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.333333333x3 + 1 + x6 = 0 + 1 Reorder the terms: -1 + 1 + -3.333333333x3 + x6 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.333333333x3 + x6 = 0 + 1 -3.333333333x3 + x6 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.333333333x3 + x6 = 1 The x term is -3.333333333x3. 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. -3.333333333x3 + 2.777777779 + x6 = 1 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x3 + x6 = 1 + 2.777777779 Combine like terms: 1 + 2.777777779 = 3.777777779 2.777777779 + -3.333333333x3 + x6 = 3.777777779 Factor a perfect square on the left side: (x3 + -1.666666667)(x3 + -1.666666667) = 3.777777779 Calculate the square root of the right side: 1.943650632 Break this problem into two subproblems by setting (x3 + -1.666666667) equal to 1.943650632 and -1.943650632.Subproblem 1
x3 + -1.666666667 = 1.943650632 Simplifying x3 + -1.666666667 = 1.943650632 Reorder the terms: -1.666666667 + x3 = 1.943650632 Solving -1.666666667 + x3 = 1.943650632 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 + x3 = 1.943650632 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x3 = 1.943650632 + 1.666666667 x3 = 1.943650632 + 1.666666667 Combine like terms: 1.943650632 + 1.666666667 = 3.610317299 x3 = 3.610317299 Simplifying x3 = 3.610317299 Reorder the terms: -3.610317299 + x3 = 3.610317299 + -3.610317299 Combine like terms: 3.610317299 + -3.610317299 = 0.000000000 -3.610317299 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + -1.666666667 = -1.943650632 Simplifying x3 + -1.666666667 = -1.943650632 Reorder the terms: -1.666666667 + x3 = -1.943650632 Solving -1.666666667 + x3 = -1.943650632 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 + x3 = -1.943650632 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x3 = -1.943650632 + 1.666666667 x3 = -1.943650632 + 1.666666667 Combine like terms: -1.943650632 + 1.666666667 = -0.276983965 x3 = -0.276983965 Simplifying x3 = -0.276983965 Reorder the terms: 0.276983965 + x3 = -0.276983965 + 0.276983965 Combine like terms: -0.276983965 + 0.276983965 = 0.000000000 0.276983965 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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