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Simplifying 6x2 + 15x + -39 = 0 Reorder the terms: -39 + 15x + 6x2 = 0 Solving -39 + 15x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + 5x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying -13 + 5x + 2x2 = 0 Solving -13 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 2.5x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 2.5x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 2.5x + x2 = 0 + 6.5 2.5x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 2.5x + x2 = 6.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 6.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 6.5 + 1.5625 Combine like terms: 6.5 + 1.5625 = 8.0625 1.5625 + 2.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + 1.25) equal to 2.839454173 and -2.839454173.Subproblem 1
x + 1.25 = 2.839454173 Simplifying x + 1.25 = 2.839454173 Reorder the terms: 1.25 + x = 2.839454173 Solving 1.25 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.839454173 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.839454173 + -1.25 x = 2.839454173 + -1.25 Combine like terms: 2.839454173 + -1.25 = 1.589454173 x = 1.589454173 Simplifying x = 1.589454173Subproblem 2
x + 1.25 = -2.839454173 Simplifying x + 1.25 = -2.839454173 Reorder the terms: 1.25 + x = -2.839454173 Solving 1.25 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.839454173 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.839454173 + -1.25 x = -2.839454173 + -1.25 Combine like terms: -2.839454173 + -1.25 = -4.089454173 x = -4.089454173 Simplifying x = -4.089454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.589454173, -4.089454173}Solution
x = {1.589454173, -4.089454173}
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