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Simplifying 9x4 + -90x3 + 8x2 = 0 Reorder the terms: 8x2 + -90x3 + 9x4 = 0 Solving 8x2 + -90x3 + 9x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(8 + -90x + 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 '(8 + -90x + 9x2)' equal to zero and attempt to solve: Simplifying 8 + -90x + 9x2 = 0 Solving 8 + -90x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + -10x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + -10x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + -10x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + -10x + x2 = 0 + -0.8888888889 -10x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 -10x + x2 = -0.8888888889 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -0.8888888889 + 25 Reorder the terms: 25 + -10x + x2 = -0.8888888889 + 25 Combine like terms: -0.8888888889 + 25 = 24.1111111111 25 + -10x + x2 = 24.1111111111 Factor a perfect square on the left side: (x + -5)(x + -5) = 24.1111111111 Calculate the square root of the right side: 4.910306621 Break this problem into two subproblems by setting (x + -5) equal to 4.910306621 and -4.910306621.Subproblem 1
x + -5 = 4.910306621 Simplifying x + -5 = 4.910306621 Reorder the terms: -5 + x = 4.910306621 Solving -5 + x = 4.910306621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.910306621 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.910306621 + 5 x = 4.910306621 + 5 Combine like terms: 4.910306621 + 5 = 9.910306621 x = 9.910306621 Simplifying x = 9.910306621Subproblem 2
x + -5 = -4.910306621 Simplifying x + -5 = -4.910306621 Reorder the terms: -5 + x = -4.910306621 Solving -5 + x = -4.910306621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.910306621 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.910306621 + 5 x = -4.910306621 + 5 Combine like terms: -4.910306621 + 5 = 0.089693379 x = 0.089693379 Simplifying x = 0.089693379Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.910306621, 0.089693379}Solution
x = {0, 9.910306621, 0.089693379}
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