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Simplifying 6x2 + -18x + -52 = 0 Reorder the terms: -52 + -18x + 6x2 = 0 Solving -52 + -18x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-26 + -9x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-26 + -9x + 3x2)' equal to zero and attempt to solve: Simplifying -26 + -9x + 3x2 = 0 Solving -26 + -9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.666666667 + -3x + x2 = 0 Move the constant term to the right: Add '8.666666667' to each side of the equation. -8.666666667 + -3x + 8.666666667 + x2 = 0 + 8.666666667 Reorder the terms: -8.666666667 + 8.666666667 + -3x + x2 = 0 + 8.666666667 Combine like terms: -8.666666667 + 8.666666667 = 0.000000000 0.000000000 + -3x + x2 = 0 + 8.666666667 -3x + x2 = 0 + 8.666666667 Combine like terms: 0 + 8.666666667 = 8.666666667 -3x + x2 = 8.666666667 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 8.666666667 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 8.666666667 + 2.25 Combine like terms: 8.666666667 + 2.25 = 10.916666667 2.25 + -3x + x2 = 10.916666667 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 10.916666667 Calculate the square root of the right side: 3.304037934 Break this problem into two subproblems by setting (x + -1.5) equal to 3.304037934 and -3.304037934.Subproblem 1
x + -1.5 = 3.304037934 Simplifying x + -1.5 = 3.304037934 Reorder the terms: -1.5 + x = 3.304037934 Solving -1.5 + x = 3.304037934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.304037934 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.304037934 + 1.5 x = 3.304037934 + 1.5 Combine like terms: 3.304037934 + 1.5 = 4.804037934 x = 4.804037934 Simplifying x = 4.804037934Subproblem 2
x + -1.5 = -3.304037934 Simplifying x + -1.5 = -3.304037934 Reorder the terms: -1.5 + x = -3.304037934 Solving -1.5 + x = -3.304037934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.304037934 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.304037934 + 1.5 x = -3.304037934 + 1.5 Combine like terms: -3.304037934 + 1.5 = -1.804037934 x = -1.804037934 Simplifying x = -1.804037934Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.804037934, -1.804037934}Solution
x = {4.804037934, -1.804037934}
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