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Simplifying 14x6 + -11x5 + 17x4 = 0 Reorder the terms: 17x4 + -11x5 + 14x6 = 0 Solving 17x4 + -11x5 + 14x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x4'. x4(17 + -11x + 14x2) = 0Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(17 + -11x + 14x2)' equal to zero and attempt to solve: Simplifying 17 + -11x + 14x2 = 0 Solving 17 + -11x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 1.214285714 + -0.7857142857x + x2 = 0 Move the constant term to the right: Add '-1.214285714' to each side of the equation. 1.214285714 + -0.7857142857x + -1.214285714 + x2 = 0 + -1.214285714 Reorder the terms: 1.214285714 + -1.214285714 + -0.7857142857x + x2 = 0 + -1.214285714 Combine like terms: 1.214285714 + -1.214285714 = 0.000000000 0.000000000 + -0.7857142857x + x2 = 0 + -1.214285714 -0.7857142857x + x2 = 0 + -1.214285714 Combine like terms: 0 + -1.214285714 = -1.214285714 -0.7857142857x + x2 = -1.214285714 The x term is -0.7857142857x. Take half its coefficient (-0.3928571429). Square it (0.1543367347) and add it to both sides. Add '0.1543367347' to each side of the equation. -0.7857142857x + 0.1543367347 + x2 = -1.214285714 + 0.1543367347 Reorder the terms: 0.1543367347 + -0.7857142857x + x2 = -1.214285714 + 0.1543367347 Combine like terms: -1.214285714 + 0.1543367347 = -1.0599489793 0.1543367347 + -0.7857142857x + x2 = -1.0599489793 Factor a perfect square on the left side: (x + -0.3928571429)(x + -0.3928571429) = -1.0599489793 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. The solution to this equation could not be determined.
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