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Simplifying 48x2 + -52x + 140 = 0 Reorder the terms: 140 + -52x + 48x2 = 0 Solving 140 + -52x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(35 + -13x + 12x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(35 + -13x + 12x2)' equal to zero and attempt to solve: Simplifying 35 + -13x + 12x2 = 0 Solving 35 + -13x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 2.916666667 + -1.083333333x + x2 = 0 Move the constant term to the right: Add '-2.916666667' to each side of the equation. 2.916666667 + -1.083333333x + -2.916666667 + x2 = 0 + -2.916666667 Reorder the terms: 2.916666667 + -2.916666667 + -1.083333333x + x2 = 0 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + -1.083333333x + x2 = 0 + -2.916666667 -1.083333333x + x2 = 0 + -2.916666667 Combine like terms: 0 + -2.916666667 = -2.916666667 -1.083333333x + x2 = -2.916666667 The x term is -1.083333333x. Take half its coefficient (-0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. -1.083333333x + 0.2934027776 + x2 = -2.916666667 + 0.2934027776 Reorder the terms: 0.2934027776 + -1.083333333x + x2 = -2.916666667 + 0.2934027776 Combine like terms: -2.916666667 + 0.2934027776 = -2.6232638894 0.2934027776 + -1.083333333x + x2 = -2.6232638894 Factor a perfect square on the left side: (x + -0.5416666665)(x + -0.5416666665) = -2.6232638894 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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