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Simplifying 6x2 + -20x + -12 = 0 Reorder the terms: -12 + -20x + 6x2 = 0 Solving -12 + -20x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -10x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -10x + 3x2)' equal to zero and attempt to solve: Simplifying -6 + -10x + 3x2 = 0 Solving -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 = 4.777777779 2.777777779 + -3.333333333x + x2 = 4.777777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 4.777777779 Calculate the square root of the right side: 2.185812842 Break this problem into two subproblems by setting (x + -1.666666667) equal to 2.185812842 and -2.185812842.Subproblem 1
x + -1.666666667 = 2.185812842 Simplifying x + -1.666666667 = 2.185812842 Reorder the terms: -1.666666667 + x = 2.185812842 Solving -1.666666667 + x = 2.185812842 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 = 2.185812842 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 2.185812842 + 1.666666667 x = 2.185812842 + 1.666666667 Combine like terms: 2.185812842 + 1.666666667 = 3.852479509 x = 3.852479509 Simplifying x = 3.852479509Subproblem 2
x + -1.666666667 = -2.185812842 Simplifying x + -1.666666667 = -2.185812842 Reorder the terms: -1.666666667 + x = -2.185812842 Solving -1.666666667 + x = -2.185812842 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 = -2.185812842 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -2.185812842 + 1.666666667 x = -2.185812842 + 1.666666667 Combine like terms: -2.185812842 + 1.666666667 = -0.519146175 x = -0.519146175 Simplifying x = -0.519146175Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.852479509, -0.519146175}Solution
x = {3.852479509, -0.519146175}
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