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Simplifying 232 = 148t + -16t2 Solving 232 = 148t + -16t2 Solving for variable 't'. Reorder the terms: 232 + -148t + 16t2 = 148t + -148t + -16t2 + 16t2 Combine like terms: 148t + -148t = 0 232 + -148t + 16t2 = 0 + -16t2 + 16t2 232 + -148t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 232 + -148t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(58 + -37t + 4t2) = 0 Factor a trinomial. 4((2 + -1t)(29 + -4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(29 + -4t)' equal to zero and attempt to solve: Simplifying 29 + -4t = 0 Solving 29 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + -4t = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -4t = 0 + -29 -4t = 0 + -29 Combine like terms: 0 + -29 = -29 -4t = -29 Divide each side by '-4'. t = 7.25 Simplifying t = 7.25Solution
t = {2, 7.25}
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