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Simplifying 20t2 + 44t + 48 = 0 Reorder the terms: 48 + 44t + 20t2 = 0 Solving 48 + 44t + 20t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(12 + 11t + 5t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(12 + 11t + 5t2)' equal to zero and attempt to solve: Simplifying 12 + 11t + 5t2 = 0 Solving 12 + 11t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 2.2t + t2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 2.2t + -2.4 + t2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 2.2t + t2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 2.2t + t2 = 0 + -2.4 2.2t + t2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 2.2t + t2 = -2.4 The t term is 2.2t. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2t + 1.21 + t2 = -2.4 + 1.21 Reorder the terms: 1.21 + 2.2t + t2 = -2.4 + 1.21 Combine like terms: -2.4 + 1.21 = -1.19 1.21 + 2.2t + t2 = -1.19 Factor a perfect square on the left side: (t + 1.1)(t + 1.1) = -1.19 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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