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Simplifying 6x2 + 20x + -6 = 0 Reorder the terms: -6 + 20x + 6x2 = 0 Solving -6 + 20x + 6x2 = 0 Solving for variable 'x'. 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 = 0.276983965 x = 0.276983965 Simplifying x = 0.276983965Subproblem 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 = -3.610317299 x = -3.610317299 Simplifying x = -3.610317299Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.276983965, -3.610317299}Solution
x = {0.276983965, -3.610317299}
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