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Simplifying 192x2 + -56x + 196 = 0 Reorder the terms: 196 + -56x + 192x2 = 0 Solving 196 + -56x + 192x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(49 + -14x + 48x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(49 + -14x + 48x2)' equal to zero and attempt to solve: Simplifying 49 + -14x + 48x2 = 0 Solving 49 + -14x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. 1.020833333 + -0.2916666667x + x2 = 0 Move the constant term to the right: Add '-1.020833333' to each side of the equation. 1.020833333 + -0.2916666667x + -1.020833333 + x2 = 0 + -1.020833333 Reorder the terms: 1.020833333 + -1.020833333 + -0.2916666667x + x2 = 0 + -1.020833333 Combine like terms: 1.020833333 + -1.020833333 = 0.000000000 0.000000000 + -0.2916666667x + x2 = 0 + -1.020833333 -0.2916666667x + x2 = 0 + -1.020833333 Combine like terms: 0 + -1.020833333 = -1.020833333 -0.2916666667x + x2 = -1.020833333 The x term is -0.2916666667x. Take half its coefficient (-0.1458333334). Square it (0.02126736113) and add it to both sides. Add '0.02126736113' to each side of the equation. -0.2916666667x + 0.02126736113 + x2 = -1.020833333 + 0.02126736113 Reorder the terms: 0.02126736113 + -0.2916666667x + x2 = -1.020833333 + 0.02126736113 Combine like terms: -1.020833333 + 0.02126736113 = -0.99956597187 0.02126736113 + -0.2916666667x + x2 = -0.99956597187 Factor a perfect square on the left side: (x + -0.1458333334)(x + -0.1458333334) = -0.99956597187 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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