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Simplifying 36x3 + 6x2 = 9x Reorder the terms: 6x2 + 36x3 = 9x Solving 6x2 + 36x3 = 9x Solving for variable 'x'. Reorder the terms: -9x + 6x2 + 36x3 = 9x + -9x Combine like terms: 9x + -9x = 0 -9x + 6x2 + 36x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-3 + 2x + 12x2) = 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 '(-3 + 2x + 12x2)' equal to zero and attempt to solve: Simplifying -3 + 2x + 12x2 = 0 Solving -3 + 2x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.25 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.1666666667x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.1666666667x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.1666666667x + x2 = 0 + 0.25 0.1666666667x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.1666666667x + x2 = 0.25 The x term is 0.1666666667x. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667x + 0.006944444447 + x2 = 0.25 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 0.25 + 0.006944444447 Combine like terms: 0.25 + 0.006944444447 = 0.256944444447 0.006944444447 + 0.1666666667x + x2 = 0.256944444447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 0.256944444447 Calculate the square root of the right side: 0.506896878 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 0.506896878 and -0.506896878.Subproblem 1
x + 0.08333333335 = 0.506896878 Simplifying x + 0.08333333335 = 0.506896878 Reorder the terms: 0.08333333335 + x = 0.506896878 Solving 0.08333333335 + x = 0.506896878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 0.506896878 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 0.506896878 + -0.08333333335 x = 0.506896878 + -0.08333333335 Combine like terms: 0.506896878 + -0.08333333335 = 0.42356354465 x = 0.42356354465 Simplifying x = 0.42356354465Subproblem 2
x + 0.08333333335 = -0.506896878 Simplifying x + 0.08333333335 = -0.506896878 Reorder the terms: 0.08333333335 + x = -0.506896878 Solving 0.08333333335 + x = -0.506896878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -0.506896878 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -0.506896878 + -0.08333333335 x = -0.506896878 + -0.08333333335 Combine like terms: -0.506896878 + -0.08333333335 = -0.59023021135 x = -0.59023021135 Simplifying x = -0.59023021135Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.42356354465, -0.59023021135}Solution
x = {0, 0.42356354465, -0.59023021135}
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