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Simplifying 48x2 + 16x + 240 = 0 Reorder the terms: 240 + 16x + 48x2 = 0 Solving 240 + 16x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(15 + x + 3x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(15 + x + 3x2)' equal to zero and attempt to solve: Simplifying 15 + x + 3x2 = 0 Solving 15 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 0.3333333333x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 0.3333333333x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 0.3333333333x + x2 = 0 + -5 0.3333333333x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 0.3333333333x + x2 = -5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = -5 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = -5 + 0.25 Combine like terms: -5 + 0.25 = -4.75 0.25 + 0.3333333333x + x2 = -4.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -4.75 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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