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Simplifying 6x2 + 39x + -81 = 0 Reorder the terms: -81 + 39x + 6x2 = 0 Solving -81 + 39x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-27 + 13x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-27 + 13x + 2x2)' equal to zero and attempt to solve: Simplifying -27 + 13x + 2x2 = 0 Solving -27 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + 6.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 6.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 6.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 6.5x + x2 = 0 + 13.5 6.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 6.5x + x2 = 13.5 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 13.5 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 13.5 + 10.5625 Combine like terms: 13.5 + 10.5625 = 24.0625 10.5625 + 6.5x + x2 = 24.0625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (x + 3.25) equal to 4.905354218 and -4.905354218.Subproblem 1
x + 3.25 = 4.905354218 Simplifying x + 3.25 = 4.905354218 Reorder the terms: 3.25 + x = 4.905354218 Solving 3.25 + x = 4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 4.905354218 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 4.905354218 + -3.25 x = 4.905354218 + -3.25 Combine like terms: 4.905354218 + -3.25 = 1.655354218 x = 1.655354218 Simplifying x = 1.655354218Subproblem 2
x + 3.25 = -4.905354218 Simplifying x + 3.25 = -4.905354218 Reorder the terms: 3.25 + x = -4.905354218 Solving 3.25 + x = -4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -4.905354218 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -4.905354218 + -3.25 x = -4.905354218 + -3.25 Combine like terms: -4.905354218 + -3.25 = -8.155354218 x = -8.155354218 Simplifying x = -8.155354218Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.655354218, -8.155354218}Solution
x = {1.655354218, -8.155354218}
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