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Simplifying 14x2 + 4x + 2 = 0 Reorder the terms: 2 + 4x + 14x2 = 0 Solving 2 + 4x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 2x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 2x + 7x2)' equal to zero and attempt to solve: Simplifying 1 + 2x + 7x2 = 0 Solving 1 + 2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.2857142857x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.2857142857x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.2857142857x + x2 = 0 + -0.1428571429 0.2857142857x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.2857142857x + x2 = -0.1428571429 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = -0.1428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = -0.1428571429 + 0.02040816328 Combine like terms: -0.1428571429 + 0.02040816328 = -0.12244897962 0.02040816328 + 0.2857142857x + x2 = -0.12244897962 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = -0.12244897962 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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