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Simplifying 21x4 + 18x2 + 36x3 = 0 Reorder the terms: 18x2 + 36x3 + 21x4 = 0 Solving 18x2 + 36x3 + 21x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(6 + 12x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(6 + 12x + 7x2)' equal to zero and attempt to solve: Simplifying 6 + 12x + 7x2 = 0 Solving 6 + 12x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 1.714285714x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 1.714285714x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 1.714285714x + x2 = 0 + -0.8571428571 1.714285714x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 1.714285714x + x2 = -0.8571428571 The x term is 1.714285714x. Take half its coefficient (0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. 1.714285714x + 0.7346938773 + x2 = -0.8571428571 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = -0.8571428571 + 0.7346938773 Combine like terms: -0.8571428571 + 0.7346938773 = -0.1224489798 0.7346938773 + 1.714285714x + x2 = -0.1224489798 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = -0.1224489798 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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