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Simplifying -6x2 + -36x + -8 = 0 Reorder the terms: -8 + -36x + -6x2 = 0 Solving -8 + -36x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + 18x + 3x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + 18x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 18x + 3x2 = 0 Solving 4 + 18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 6x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 6x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 6x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 6x + x2 = 0 + -1.333333333 6x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 6x + x2 = -1.333333333 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -1.333333333 + 9 Reorder the terms: 9 + 6x + x2 = -1.333333333 + 9 Combine like terms: -1.333333333 + 9 = 7.666666667 9 + 6x + x2 = 7.666666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 7.666666667 Calculate the square root of the right side: 2.768874621 Break this problem into two subproblems by setting (x + 3) equal to 2.768874621 and -2.768874621.Subproblem 1
x + 3 = 2.768874621 Simplifying x + 3 = 2.768874621 Reorder the terms: 3 + x = 2.768874621 Solving 3 + x = 2.768874621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.768874621 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.768874621 + -3 x = 2.768874621 + -3 Combine like terms: 2.768874621 + -3 = -0.231125379 x = -0.231125379 Simplifying x = -0.231125379Subproblem 2
x + 3 = -2.768874621 Simplifying x + 3 = -2.768874621 Reorder the terms: 3 + x = -2.768874621 Solving 3 + x = -2.768874621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.768874621 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.768874621 + -3 x = -2.768874621 + -3 Combine like terms: -2.768874621 + -3 = -5.768874621 x = -5.768874621 Simplifying x = -5.768874621Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.231125379, -5.768874621}Solution
x = {-0.231125379, -5.768874621}
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