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Simplifying 6x2 + -6 = 20x Reorder the terms: -6 + 6x2 = 20x Solving -6 + 6x2 = 20x Solving for variable 'x'. Reorder the terms: -6 + -20x + 6x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -6 + -20x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -10x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -10x + 3x2)' equal to zero and attempt to solve: Simplifying -3 + -10x + 3x2 = 0 Solving -3 + -10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -3.333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.333333333x + x2 = 0 + 1 -3.333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.333333333x + x2 = 1 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 = 1 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 1 + 2.777777779 Combine like terms: 1 + 2.777777779 = 3.777777779 2.777777779 + -3.333333333x + x2 = 3.777777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 3.777777779 Calculate the square root of the right side: 1.943650632 Break this problem into two subproblems by setting (x + -1.666666667) equal to 1.943650632 and -1.943650632.Subproblem 1
x + -1.666666667 = 1.943650632 Simplifying x + -1.666666667 = 1.943650632 Reorder the terms: -1.666666667 + x = 1.943650632 Solving -1.666666667 + x = 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 + x = 1.943650632 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 1.943650632 + 1.666666667 x = 1.943650632 + 1.666666667 Combine like terms: 1.943650632 + 1.666666667 = 3.610317299 x = 3.610317299 Simplifying x = 3.610317299Subproblem 2
x + -1.666666667 = -1.943650632 Simplifying x + -1.666666667 = -1.943650632 Reorder the terms: -1.666666667 + x = -1.943650632 Solving -1.666666667 + x = -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 + x = -1.943650632 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -1.943650632 + 1.666666667 x = -1.943650632 + 1.666666667 Combine like terms: -1.943650632 + 1.666666667 = -0.276983965 x = -0.276983965 Simplifying x = -0.276983965Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.610317299, -0.276983965}Solution
x = {3.610317299, -0.276983965}
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