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Simplifying -3x2 + 39x + -6 = 0 Reorder the terms: -6 + 39x + -3x2 = 0 Solving -6 + 39x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 13x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 13x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + 13x + -1x2 = 0 Solving -2 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -13x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -13x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -13x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -13x + x2 = 0 + -2 -13x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -13x + x2 = -2 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -2 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -2 + 42.25 Combine like terms: -2 + 42.25 = 40.25 42.25 + -13x + x2 = 40.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + -6.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + -6.5 = 6.34428877 Simplifying x + -6.5 = 6.34428877 Reorder the terms: -6.5 + x = 6.34428877 Solving -6.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.34428877 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.34428877 + 6.5 x = 6.34428877 + 6.5 Combine like terms: 6.34428877 + 6.5 = 12.84428877 x = 12.84428877 Simplifying x = 12.84428877Subproblem 2
x + -6.5 = -6.34428877 Simplifying x + -6.5 = -6.34428877 Reorder the terms: -6.5 + x = -6.34428877 Solving -6.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.34428877 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.34428877 + 6.5 x = -6.34428877 + 6.5 Combine like terms: -6.34428877 + 6.5 = 0.15571123 x = 0.15571123 Simplifying x = 0.15571123Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.84428877, 0.15571123}Solution
x = {12.84428877, 0.15571123}
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