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Simplifying 48x2 + -32x + 60 = 0 Reorder the terms: 60 + -32x + 48x2 = 0 Solving 60 + -32x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(15 + -8x + 12x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(15 + -8x + 12x2)' equal to zero and attempt to solve: Simplifying 15 + -8x + 12x2 = 0 Solving 15 + -8x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1.25 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -0.6666666667x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -0.6666666667x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -0.6666666667x + x2 = 0 + -1.25 -0.6666666667x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -0.6666666667x + x2 = -1.25 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -1.25 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -1.25 + 0.1111111112 Combine like terms: -1.25 + 0.1111111112 = -1.1388888888 0.1111111112 + -0.6666666667x + x2 = -1.1388888888 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -1.1388888888 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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