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Simplifying 12x4 + -27x3 = 6x2 Reorder the terms: -27x3 + 12x4 = 6x2 Solving -27x3 + 12x4 = 6x2 Solving for variable 'x'. Reorder the terms: -6x2 + -27x3 + 12x4 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -6x2 + -27x3 + 12x4 = 0 Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(-2 + -9x + 4x2) = 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 '(-2 + -9x + 4x2)' equal to zero and attempt to solve: Simplifying -2 + -9x + 4x2 = 0 Solving -2 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + -2.25x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.25x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.25x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.25x + x2 = 0 + 0.5 -2.25x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.25x + x2 = 0.5 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 0.5 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 0.5 + 1.265625 Combine like terms: 0.5 + 1.265625 = 1.765625 1.265625 + -2.25x + x2 = 1.765625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x + -1.125) equal to 1.328768227 and -1.328768227.Subproblem 1
x + -1.125 = 1.328768227 Simplifying x + -1.125 = 1.328768227 Reorder the terms: -1.125 + x = 1.328768227 Solving -1.125 + x = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.328768227 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.328768227 + 1.125 x = 1.328768227 + 1.125 Combine like terms: 1.328768227 + 1.125 = 2.453768227 x = 2.453768227 Simplifying x = 2.453768227Subproblem 2
x + -1.125 = -1.328768227 Simplifying x + -1.125 = -1.328768227 Reorder the terms: -1.125 + x = -1.328768227 Solving -1.125 + x = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.328768227 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.328768227 + 1.125 x = -1.328768227 + 1.125 Combine like terms: -1.328768227 + 1.125 = -0.203768227 x = -0.203768227 Simplifying x = -0.203768227Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.453768227, -0.203768227}Solution
x = {0, 2.453768227, -0.203768227}
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