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Simplifying 14x2 + 60x + 166 = 0 Reorder the terms: 166 + 60x + 14x2 = 0 Solving 166 + 60x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(83 + 30x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(83 + 30x + 7x2)' equal to zero and attempt to solve: Simplifying 83 + 30x + 7x2 = 0 Solving 83 + 30x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 11.85714286 + 4.285714286x + x2 = 0 Move the constant term to the right: Add '-11.85714286' to each side of the equation. 11.85714286 + 4.285714286x + -11.85714286 + x2 = 0 + -11.85714286 Reorder the terms: 11.85714286 + -11.85714286 + 4.285714286x + x2 = 0 + -11.85714286 Combine like terms: 11.85714286 + -11.85714286 = 0.00000000 0.00000000 + 4.285714286x + x2 = 0 + -11.85714286 4.285714286x + x2 = 0 + -11.85714286 Combine like terms: 0 + -11.85714286 = -11.85714286 4.285714286x + x2 = -11.85714286 The x term is 4.285714286x. Take half its coefficient (2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. 4.285714286x + 4.591836735 + x2 = -11.85714286 + 4.591836735 Reorder the terms: 4.591836735 + 4.285714286x + x2 = -11.85714286 + 4.591836735 Combine like terms: -11.85714286 + 4.591836735 = -7.265306125 4.591836735 + 4.285714286x + x2 = -7.265306125 Factor a perfect square on the left side: (x + 2.142857143)(x + 2.142857143) = -7.265306125 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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