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Simplifying 14x2 + 4x + 4 = 0 Reorder the terms: 4 + 4x + 14x2 = 0 Solving 4 + 4x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 2x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 2x + 7x2)' equal to zero and attempt to solve: Simplifying 2 + 2x + 7x2 = 0 Solving 2 + 2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 0.2857142857x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 0.2857142857x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 0.2857142857x + x2 = 0 + -0.2857142857 0.2857142857x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 0.2857142857x + x2 = -0.2857142857 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 = -0.2857142857 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = -0.2857142857 + 0.02040816328 Combine like terms: -0.2857142857 + 0.02040816328 = -0.26530612242 0.02040816328 + 0.2857142857x + x2 = -0.26530612242 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = -0.26530612242 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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