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Simplifying 14x2 + -8x + 6 = 0 Reorder the terms: 6 + -8x + 14x2 = 0 Solving 6 + -8x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -4x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -4x + 7x2)' equal to zero and attempt to solve: Simplifying 3 + -4x + 7x2 = 0 Solving 3 + -4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.5714285714x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + -0.5714285714x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + -0.4285714286 -0.5714285714x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 -0.5714285714x + x2 = -0.4285714286 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = -0.4285714286 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = -0.4285714286 + 0.08163265305 Combine like terms: -0.4285714286 + 0.08163265305 = -0.34693877555 0.08163265305 + -0.5714285714x + x2 = -0.34693877555 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = -0.34693877555 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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