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Simplifying 42x4 + -18x3 + 16x2 = 0 Reorder the terms: 16x2 + -18x3 + 42x4 = 0 Solving 16x2 + -18x3 + 42x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(8 + -9x + 21x2) = 0 Ignore the factor 2.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 '(8 + -9x + 21x2)' equal to zero and attempt to solve: Simplifying 8 + -9x + 21x2 = 0 Solving 8 + -9x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.380952381 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '-0.380952381' to each side of the equation. 0.380952381 + -0.4285714286x + -0.380952381 + x2 = 0 + -0.380952381 Reorder the terms: 0.380952381 + -0.380952381 + -0.4285714286x + x2 = 0 + -0.380952381 Combine like terms: 0.380952381 + -0.380952381 = 0.000000000 0.000000000 + -0.4285714286x + x2 = 0 + -0.380952381 -0.4285714286x + x2 = 0 + -0.380952381 Combine like terms: 0 + -0.380952381 = -0.380952381 -0.4285714286x + x2 = -0.380952381 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = -0.380952381 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = -0.380952381 + 0.04591836735 Combine like terms: -0.380952381 + 0.04591836735 = -0.33503401365 0.04591836735 + -0.4285714286x + x2 = -0.33503401365 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = -0.33503401365 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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