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Simplifying 14x2 + 2x + 12 = 6 Reorder the terms: 12 + 2x + 14x2 = 6 Solving 12 + 2x + 14x2 = 6 Solving for variable 'x'. Reorder the terms: 12 + -6 + 2x + 14x2 = 6 + -6 Combine like terms: 12 + -6 = 6 6 + 2x + 14x2 = 6 + -6 Combine like terms: 6 + -6 = 0 6 + 2x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + x + 7x2)' equal to zero and attempt to solve: Simplifying 3 + x + 7x2 = 0 Solving 3 + x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + 0.1428571429x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + 0.1428571429x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + 0.1428571429x + x2 = 0 + -0.4285714286 0.1428571429x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 0.1428571429x + x2 = -0.4285714286 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1428571429x + 0.25 + x2 = -0.4285714286 + 0.25 Reorder the terms: 0.25 + 0.1428571429x + x2 = -0.4285714286 + 0.25 Combine like terms: -0.4285714286 + 0.25 = -0.1785714286 0.25 + 0.1428571429x + x2 = -0.1785714286 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.1785714286 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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