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Simplifying 11535 = -100t2 + 569t + 11535 Reorder the terms: 11535 = 11535 + 569t + -100t2 Add '-11535' to each side of the equation. 11535 + -11535 = 11535 + 569t + -11535 + -100t2 Combine like terms: 11535 + -11535 = 0 0 = 11535 + 569t + -11535 + -100t2 Reorder the terms: 0 = 11535 + -11535 + 569t + -100t2 Combine like terms: 11535 + -11535 = 0 0 = 0 + 569t + -100t2 0 = 569t + -100t2 Solving 0 = 569t + -100t2 Solving for variable 't'. Remove the zero: -569t + 100t2 = 569t + -100t2 + -569t + 100t2 Reorder the terms: -569t + 100t2 = 569t + -569t + -100t2 + 100t2 Combine like terms: 569t + -569t = 0 -569t + 100t2 = 0 + -100t2 + 100t2 -569t + 100t2 = -100t2 + 100t2 Combine like terms: -100t2 + 100t2 = 0 -569t + 100t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-569 + 100t) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-569 + 100t)' equal to zero and attempt to solve: Simplifying -569 + 100t = 0 Solving -569 + 100t = 0 Move all terms containing t to the left, all other terms to the right. Add '569' to each side of the equation. -569 + 569 + 100t = 0 + 569 Combine like terms: -569 + 569 = 0 0 + 100t = 0 + 569 100t = 0 + 569 Combine like terms: 0 + 569 = 569 100t = 569 Divide each side by '100'. t = 5.69 Simplifying t = 5.69Solution
t = {0, 5.69}
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