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Simplifying 3x3 + 36x2 = 35x4 Reorder the terms: 36x2 + 3x3 = 35x4 Solving 36x2 + 3x3 = 35x4 Solving for variable 'x'. Combine like terms: 35x4 + -35x4 = 0 36x2 + 3x3 + -35x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(36 + 3x + -35x2) = 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 '(36 + 3x + -35x2)' equal to zero and attempt to solve: Simplifying 36 + 3x + -35x2 = 0 Solving 36 + 3x + -35x2 = 0 Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. -1.028571429 + -0.08571428571x + x2 = 0 Move the constant term to the right: Add '1.028571429' to each side of the equation. -1.028571429 + -0.08571428571x + 1.028571429 + x2 = 0 + 1.028571429 Reorder the terms: -1.028571429 + 1.028571429 + -0.08571428571x + x2 = 0 + 1.028571429 Combine like terms: -1.028571429 + 1.028571429 = 0.000000000 0.000000000 + -0.08571428571x + x2 = 0 + 1.028571429 -0.08571428571x + x2 = 0 + 1.028571429 Combine like terms: 0 + 1.028571429 = 1.028571429 -0.08571428571x + x2 = 1.028571429 The x term is -0.08571428571x. Take half its coefficient (-0.04285714286). Square it (0.001836734694) and add it to both sides. Add '0.001836734694' to each side of the equation. -0.08571428571x + 0.001836734694 + x2 = 1.028571429 + 0.001836734694 Reorder the terms: 0.001836734694 + -0.08571428571x + x2 = 1.028571429 + 0.001836734694 Combine like terms: 1.028571429 + 0.001836734694 = 1.030408163694 0.001836734694 + -0.08571428571x + x2 = 1.030408163694 Factor a perfect square on the left side: (x + -0.04285714286)(x + -0.04285714286) = 1.030408163694 Calculate the square root of the right side: 1.015090224 Break this problem into two subproblems by setting (x + -0.04285714286) equal to 1.015090224 and -1.015090224.Subproblem 1
x + -0.04285714286 = 1.015090224 Simplifying x + -0.04285714286 = 1.015090224 Reorder the terms: -0.04285714286 + x = 1.015090224 Solving -0.04285714286 + x = 1.015090224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04285714286' to each side of the equation. -0.04285714286 + 0.04285714286 + x = 1.015090224 + 0.04285714286 Combine like terms: -0.04285714286 + 0.04285714286 = 0.00000000000 0.00000000000 + x = 1.015090224 + 0.04285714286 x = 1.015090224 + 0.04285714286 Combine like terms: 1.015090224 + 0.04285714286 = 1.05794736686 x = 1.05794736686 Simplifying x = 1.05794736686Subproblem 2
x + -0.04285714286 = -1.015090224 Simplifying x + -0.04285714286 = -1.015090224 Reorder the terms: -0.04285714286 + x = -1.015090224 Solving -0.04285714286 + x = -1.015090224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04285714286' to each side of the equation. -0.04285714286 + 0.04285714286 + x = -1.015090224 + 0.04285714286 Combine like terms: -0.04285714286 + 0.04285714286 = 0.00000000000 0.00000000000 + x = -1.015090224 + 0.04285714286 x = -1.015090224 + 0.04285714286 Combine like terms: -1.015090224 + 0.04285714286 = -0.97223308114 x = -0.97223308114 Simplifying x = -0.97223308114Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.05794736686, -0.97223308114}Solution
x = {0, 1.05794736686, -0.97223308114}
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