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Simplifying (5x2) + (7x3) + (9x4) = 0 Solving (5x2) + (7x3) + (9x4) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(5 + (7x) + (9x2)) = 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 '(5 + (7x) + (9x2))' equal to zero and attempt to solve: Simplifying 5 + (7x) + (9x2) = 0 Solving 5 + (7x) + (9x2) = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + (0.7777777778x) + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + (0.7777777778x) + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + (0.7777777778x) + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + (0.7777777778x) + x2 = 0 + -0.5555555556 (0.7777777778x) + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 (0.7777777778x) + x2 = -0.5555555556 The x term is (0.7777777778x). Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. (0.7777777778x) + 0.1512345679 + x2 = -0.5555555556 + 0.1512345679 Reorder the terms: 0.1512345679 + (0.7777777778x) + x2 = -0.5555555556 + 0.1512345679 Combine like terms: -0.5555555556 + 0.1512345679 = -0.4043209877 0.1512345679 + (0.7777777778x) + x2 = -0.4043209877 Factor a perfect square on the left side: ((x) + 0.3888888889)((x) + 0.3888888889) = -0.4043209877 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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