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Simplifying 55t + -5t2 = 160 Solving 55t + -5t2 = 160 Solving for variable 't'. Reorder the terms: -160 + 55t + -5t2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + 55t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-32 + 11t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-32 + 11t + -1t2)' equal to zero and attempt to solve: Simplifying -32 + 11t + -1t2 = 0 Solving -32 + 11t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 32 + -11t + t2 = 0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + -11t + -32 + t2 = 0 + -32 Reorder the terms: 32 + -32 + -11t + t2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -11t + t2 = 0 + -32 -11t + t2 = 0 + -32 Combine like terms: 0 + -32 = -32 -11t + t2 = -32 The t term is -11t. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11t + 30.25 + t2 = -32 + 30.25 Reorder the terms: 30.25 + -11t + t2 = -32 + 30.25 Combine like terms: -32 + 30.25 = -1.75 30.25 + -11t + t2 = -1.75 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = -1.75 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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