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Simplifying 14x4 + -6x3 + 2x2 = 0 Reorder the terms: 2x2 + -6x3 + 14x4 = 0 Solving 2x2 + -6x3 + 14x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(1 + -3x + 7x2) = 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 '(1 + -3x + 7x2)' equal to zero and attempt to solve: Simplifying 1 + -3x + 7x2 = 0 Solving 1 + -3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.4285714286x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -0.4285714286x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -0.4285714286x + x2 = 0 + -0.1428571429 -0.4285714286x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -0.4285714286x + x2 = -0.1428571429 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 = -0.1428571429 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = -0.1428571429 + 0.04591836735 Combine like terms: -0.1428571429 + 0.04591836735 = -0.09693877555 0.04591836735 + -0.4285714286x + x2 = -0.09693877555 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = -0.09693877555 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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