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Simplifying 120 = 45t + -5t2 Solving 120 = 45t + -5t2 Solving for variable 't'. Reorder the terms: 120 + -45t + 5t2 = 45t + -45t + -5t2 + 5t2 Combine like terms: 45t + -45t = 0 120 + -45t + 5t2 = 0 + -5t2 + 5t2 120 + -45t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 120 + -45t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(24 + -9t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(24 + -9t + t2)' equal to zero and attempt to solve: Simplifying 24 + -9t + t2 = 0 Solving 24 + -9t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -9t + -24 + t2 = 0 + -24 Reorder the terms: 24 + -24 + -9t + t2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -9t + t2 = 0 + -24 -9t + t2 = 0 + -24 Combine like terms: 0 + -24 = -24 -9t + t2 = -24 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = -24 + 20.25 Reorder the terms: 20.25 + -9t + t2 = -24 + 20.25 Combine like terms: -24 + 20.25 = -3.75 20.25 + -9t + t2 = -3.75 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = -3.75 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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