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Simplifying 6x3 + -39x2 + -30x = 0 Reorder the terms: -30x + -39x2 + 6x3 = 0 Solving -30x + -39x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-10 + -13x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-10 + -13x + 2x2)' equal to zero and attempt to solve: Simplifying -10 + -13x + 2x2 = 0 Solving -10 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + -6.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -6.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -6.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6.5x + x2 = 0 + 5 -6.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -6.5x + x2 = 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 = 5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 5 + 10.5625 Combine like terms: 5 + 10.5625 = 15.5625 10.5625 + -6.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + -3.25) equal to 3.94493346 and -3.94493346.Subproblem 1
x + -3.25 = 3.94493346 Simplifying x + -3.25 = 3.94493346 Reorder the terms: -3.25 + x = 3.94493346 Solving -3.25 + x = 3.94493346 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 = 3.94493346 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.94493346 + 3.25 x = 3.94493346 + 3.25 Combine like terms: 3.94493346 + 3.25 = 7.19493346 x = 7.19493346 Simplifying x = 7.19493346Subproblem 2
x + -3.25 = -3.94493346 Simplifying x + -3.25 = -3.94493346 Reorder the terms: -3.25 + x = -3.94493346 Solving -3.25 + x = -3.94493346 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 = -3.94493346 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.94493346 + 3.25 x = -3.94493346 + 3.25 Combine like terms: -3.94493346 + 3.25 = -0.69493346 x = -0.69493346 Simplifying x = -0.69493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.19493346, -0.69493346}Solution
x = {0, 7.19493346, -0.69493346}
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