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Simplifying 0 = -4(4t2 + -3t + -52) Reorder the terms: 0 = -4(-52 + -3t + 4t2) 0 = (-52 * -4 + -3t * -4 + 4t2 * -4) 0 = (208 + 12t + -16t2) Solving 0 = 208 + 12t + -16t2 Solving for variable 't'. Combine like terms: 0 + -208 = -208 -208 + -12t + 16t2 = 208 + 12t + -16t2 + -208 + -12t + 16t2 Reorder the terms: -208 + -12t + 16t2 = 208 + -208 + 12t + -12t + -16t2 + 16t2 Combine like terms: 208 + -208 = 0 -208 + -12t + 16t2 = 0 + 12t + -12t + -16t2 + 16t2 -208 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 -208 + -12t + 16t2 = 0 + -16t2 + 16t2 -208 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -208 + -12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-52 + -3t + 4t2) = 0 Factor a trinomial. 4((-13 + -4t)(4 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-13 + -4t)' equal to zero and attempt to solve: Simplifying -13 + -4t = 0 Solving -13 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -4t = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4t = 0 + 13 -4t = 0 + 13 Combine like terms: 0 + 13 = 13 -4t = 13 Divide each side by '-4'. t = -3.25 Simplifying t = -3.25Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-3.25, 4}
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