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Simplifying 6x3 + 5x2 + -36x = 0 Reorder the terms: -36x + 5x2 + 6x3 = 0 Solving -36x + 5x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-36 + 5x + 6x2) = 0Subproblem 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 '(-36 + 5x + 6x2)' equal to zero and attempt to solve: Simplifying -36 + 5x + 6x2 = 0 Solving -36 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 0.8333333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 0.8333333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 0.8333333333x + x2 = 0 + 6 0.8333333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 0.8333333333x + x2 = 6 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 6 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 6 + 0.1736111111 Combine like terms: 6 + 0.1736111111 = 6.1736111111 0.1736111111 + 0.8333333333x + x2 = 6.1736111111 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 6.1736111111 Calculate the square root of the right side: 2.484675253 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 2.484675253 and -2.484675253.Subproblem 1
x + 0.4166666667 = 2.484675253 Simplifying x + 0.4166666667 = 2.484675253 Reorder the terms: 0.4166666667 + x = 2.484675253 Solving 0.4166666667 + x = 2.484675253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 2.484675253 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 2.484675253 + -0.4166666667 x = 2.484675253 + -0.4166666667 Combine like terms: 2.484675253 + -0.4166666667 = 2.0680085863 x = 2.0680085863 Simplifying x = 2.0680085863Subproblem 2
x + 0.4166666667 = -2.484675253 Simplifying x + 0.4166666667 = -2.484675253 Reorder the terms: 0.4166666667 + x = -2.484675253 Solving 0.4166666667 + x = -2.484675253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -2.484675253 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -2.484675253 + -0.4166666667 x = -2.484675253 + -0.4166666667 Combine like terms: -2.484675253 + -0.4166666667 = -2.9013419197 x = -2.9013419197 Simplifying x = -2.9013419197Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0680085863, -2.9013419197}Solution
x = {0, 2.0680085863, -2.9013419197}
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