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Simplifying 27x3 + -6x2 = 12x Reorder the terms: -6x2 + 27x3 = 12x Solving -6x2 + 27x3 = 12x Solving for variable 'x'. Reorder the terms: -12x + -6x2 + 27x3 = 12x + -12x Combine like terms: 12x + -12x = 0 -12x + -6x2 + 27x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-4 + -2x + 9x2) = 0 Ignore the factor 3.Subproblem 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 '(-4 + -2x + 9x2)' equal to zero and attempt to solve: Simplifying -4 + -2x + 9x2 = 0 Solving -4 + -2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -0.2222222222x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -0.2222222222x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -0.2222222222x + x2 = 0 + 0.4444444444 -0.2222222222x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -0.2222222222x + x2 = 0.4444444444 The x term is -0.2222222222x. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x + 0.01234567901 + x2 = 0.4444444444 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 0.4444444444 + 0.01234567901 Combine like terms: 0.4444444444 + 0.01234567901 = 0.45679012341 0.01234567901 + -0.2222222222x + x2 = 0.45679012341 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 0.45679012341 Calculate the square root of the right side: 0.675862503 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 0.675862503 and -0.675862503.Subproblem 1
x + -0.1111111111 = 0.675862503 Simplifying x + -0.1111111111 = 0.675862503 Reorder the terms: -0.1111111111 + x = 0.675862503 Solving -0.1111111111 + x = 0.675862503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = 0.675862503 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 0.675862503 + 0.1111111111 x = 0.675862503 + 0.1111111111 Combine like terms: 0.675862503 + 0.1111111111 = 0.7869736141 x = 0.7869736141 Simplifying x = 0.7869736141Subproblem 2
x + -0.1111111111 = -0.675862503 Simplifying x + -0.1111111111 = -0.675862503 Reorder the terms: -0.1111111111 + x = -0.675862503 Solving -0.1111111111 + x = -0.675862503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = -0.675862503 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -0.675862503 + 0.1111111111 x = -0.675862503 + 0.1111111111 Combine like terms: -0.675862503 + 0.1111111111 = -0.5647513919 x = -0.5647513919 Simplifying x = -0.5647513919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7869736141, -0.5647513919}Solution
x = {0, 0.7869736141, -0.5647513919}
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