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Simplifying 36x4 + -30x3 + 25x2 = 0 Reorder the terms: 25x2 + -30x3 + 36x4 = 0 Solving 25x2 + -30x3 + 36x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(25 + -30x + 36x2) = 0Subproblem 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 '(25 + -30x + 36x2)' equal to zero and attempt to solve: Simplifying 25 + -30x + 36x2 = 0 Solving 25 + -30x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.6944444444 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '-0.6944444444' to each side of the equation. 0.6944444444 + -0.8333333333x + -0.6944444444 + x2 = 0 + -0.6944444444 Reorder the terms: 0.6944444444 + -0.6944444444 + -0.8333333333x + x2 = 0 + -0.6944444444 Combine like terms: 0.6944444444 + -0.6944444444 = 0.0000000000 0.0000000000 + -0.8333333333x + x2 = 0 + -0.6944444444 -0.8333333333x + x2 = 0 + -0.6944444444 Combine like terms: 0 + -0.6944444444 = -0.6944444444 -0.8333333333x + x2 = -0.6944444444 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 = -0.6944444444 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = -0.6944444444 + 0.1736111111 Combine like terms: -0.6944444444 + 0.1736111111 = -0.5208333333 0.1736111111 + -0.8333333333x + x2 = -0.5208333333 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = -0.5208333333 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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