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Simplifying 3x2 + 15x3 + -27x4 = 0 Solving 3x2 + 15x3 + -27x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(1 + 5x + -9x2) = 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 '(1 + 5x + -9x2)' equal to zero and attempt to solve: Simplifying 1 + 5x + -9x2 = 0 Solving 1 + 5x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.1111111111 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.5555555556x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.5555555556x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.5555555556x + x2 = 0 + 0.1111111111 -0.5555555556x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.5555555556x + x2 = 0.1111111111 The x term is -0.5555555556x. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556x + 0.07716049384 + x2 = 0.1111111111 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 0.1111111111 + 0.07716049384 Combine like terms: 0.1111111111 + 0.07716049384 = 0.18827160494 0.07716049384 + -0.5555555556x + x2 = 0.18827160494 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 0.18827160494 Calculate the square root of the right side: 0.43390276 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 0.43390276 and -0.43390276.Subproblem 1
x + -0.2777777778 = 0.43390276 Simplifying x + -0.2777777778 = 0.43390276 Reorder the terms: -0.2777777778 + x = 0.43390276 Solving -0.2777777778 + x = 0.43390276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = 0.43390276 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 0.43390276 + 0.2777777778 x = 0.43390276 + 0.2777777778 Combine like terms: 0.43390276 + 0.2777777778 = 0.7116805378 x = 0.7116805378 Simplifying x = 0.7116805378Subproblem 2
x + -0.2777777778 = -0.43390276 Simplifying x + -0.2777777778 = -0.43390276 Reorder the terms: -0.2777777778 + x = -0.43390276 Solving -0.2777777778 + x = -0.43390276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = -0.43390276 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -0.43390276 + 0.2777777778 x = -0.43390276 + 0.2777777778 Combine like terms: -0.43390276 + 0.2777777778 = -0.1561249822 x = -0.1561249822 Simplifying x = -0.1561249822Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7116805378, -0.1561249822}Solution
x = {0, 0.7116805378, -0.1561249822}
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