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Simplifying 12x4 + -17x3 + 2x2 = 0 Reorder the terms: 2x2 + -17x3 + 12x4 = 0 Solving 2x2 + -17x3 + 12x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(2 + -17x + 12x2) = 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 '(2 + -17x + 12x2)' equal to zero and attempt to solve: Simplifying 2 + -17x + 12x2 = 0 Solving 2 + -17x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.1666666667 + -1.416666667x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -1.416666667x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -1.416666667x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -1.416666667x + x2 = 0 + -0.1666666667 -1.416666667x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -1.416666667x + x2 = -0.1666666667 The x term is -1.416666667x. Take half its coefficient (-0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. -1.416666667x + 0.5017361113 + x2 = -0.1666666667 + 0.5017361113 Reorder the terms: 0.5017361113 + -1.416666667x + x2 = -0.1666666667 + 0.5017361113 Combine like terms: -0.1666666667 + 0.5017361113 = 0.3350694446 0.5017361113 + -1.416666667x + x2 = 0.3350694446 Factor a perfect square on the left side: (x + -0.7083333335)(x + -0.7083333335) = 0.3350694446 Calculate the square root of the right side: 0.578851833 Break this problem into two subproblems by setting (x + -0.7083333335) equal to 0.578851833 and -0.578851833.Subproblem 1
x + -0.7083333335 = 0.578851833 Simplifying x + -0.7083333335 = 0.578851833 Reorder the terms: -0.7083333335 + x = 0.578851833 Solving -0.7083333335 + x = 0.578851833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + x = 0.578851833 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = 0.578851833 + 0.7083333335 x = 0.578851833 + 0.7083333335 Combine like terms: 0.578851833 + 0.7083333335 = 1.2871851665 x = 1.2871851665 Simplifying x = 1.2871851665Subproblem 2
x + -0.7083333335 = -0.578851833 Simplifying x + -0.7083333335 = -0.578851833 Reorder the terms: -0.7083333335 + x = -0.578851833 Solving -0.7083333335 + x = -0.578851833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + x = -0.578851833 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = -0.578851833 + 0.7083333335 x = -0.578851833 + 0.7083333335 Combine like terms: -0.578851833 + 0.7083333335 = 0.1294815005 x = 0.1294815005 Simplifying x = 0.1294815005Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2871851665, 0.1294815005}Solution
x = {0, 1.2871851665, 0.1294815005}
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