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Simplifying 420 + -112x + 12x2 = 0 Solving 420 + -112x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(105 + -28x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(105 + -28x + 3x2)' equal to zero and attempt to solve: Simplifying 105 + -28x + 3x2 = 0 Solving 105 + -28x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 35 + -9.333333333x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + -9.333333333x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -9.333333333x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -9.333333333x + x2 = 0 + -35 -9.333333333x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -9.333333333x + x2 = -35 The x term is -9.333333333x. Take half its coefficient (-4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. -9.333333333x + 21.77777778 + x2 = -35 + 21.77777778 Reorder the terms: 21.77777778 + -9.333333333x + x2 = -35 + 21.77777778 Combine like terms: -35 + 21.77777778 = -13.22222222 21.77777778 + -9.333333333x + x2 = -13.22222222 Factor a perfect square on the left side: (x + -4.666666667)(x + -4.666666667) = -13.22222222 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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