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Simplifying 9x3 + 4x2 + -1x = 0 Reorder the terms: -1x + 4x2 + 9x3 = 0 Solving -1x + 4x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 4x + 9x2) = 0Subproblem 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 '(-1 + 4x + 9x2)' equal to zero and attempt to solve: Simplifying -1 + 4x + 9x2 = 0 Solving -1 + 4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.1111111111 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.4444444444x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 0.4444444444x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 0.4444444444x + x2 = 0 + 0.1111111111 0.4444444444x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 0.4444444444x + x2 = 0.1111111111 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 0.1111111111 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 0.1111111111 + 0.04938271604 Combine like terms: 0.1111111111 + 0.04938271604 = 0.16049382714 0.04938271604 + 0.4444444444x + x2 = 0.16049382714 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 0.16049382714 Calculate the square root of the right side: 0.400616808 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 0.400616808 and -0.400616808.Subproblem 1
x + 0.2222222222 = 0.400616808 Simplifying x + 0.2222222222 = 0.400616808 Reorder the terms: 0.2222222222 + x = 0.400616808 Solving 0.2222222222 + x = 0.400616808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 0.400616808 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 0.400616808 + -0.2222222222 x = 0.400616808 + -0.2222222222 Combine like terms: 0.400616808 + -0.2222222222 = 0.1783945858 x = 0.1783945858 Simplifying x = 0.1783945858Subproblem 2
x + 0.2222222222 = -0.400616808 Simplifying x + 0.2222222222 = -0.400616808 Reorder the terms: 0.2222222222 + x = -0.400616808 Solving 0.2222222222 + x = -0.400616808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -0.400616808 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -0.400616808 + -0.2222222222 x = -0.400616808 + -0.2222222222 Combine like terms: -0.400616808 + -0.2222222222 = -0.6228390302 x = -0.6228390302 Simplifying x = -0.6228390302Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1783945858, -0.6228390302}Solution
x = {0, 0.1783945858, -0.6228390302}
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