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Simplifying 5t(5 + -1t) = 200 (5 * 5t + -1t * 5t) = 200 (25t + -5t2) = 200 Solving 25t + -5t2 = 200 Solving for variable 't'. Reorder the terms: -200 + 25t + -5t2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 25t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-40 + 5t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-40 + 5t + -1t2)' equal to zero and attempt to solve: Simplifying -40 + 5t + -1t2 = 0 Solving -40 + 5t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 40 + -5t + t2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -5t + -40 + t2 = 0 + -40 Reorder the terms: 40 + -40 + -5t + t2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -5t + t2 = 0 + -40 -5t + t2 = 0 + -40 Combine like terms: 0 + -40 = -40 -5t + t2 = -40 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -40 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -40 + 6.25 Combine like terms: -40 + 6.25 = -33.75 6.25 + -5t + t2 = -33.75 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = -33.75 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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