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Simplifying 128 = 128t + -32t2 Solving 128 = 128t + -32t2 Solving for variable 't'. Reorder the terms: 128 + -128t + 32t2 = 128t + -128t + -32t2 + 32t2 Combine like terms: 128t + -128t = 0 128 + -128t + 32t2 = 0 + -32t2 + 32t2 128 + -128t + 32t2 = -32t2 + 32t2 Combine like terms: -32t2 + 32t2 = 0 128 + -128t + 32t2 = 0 Factor out the Greatest Common Factor (GCF), '32'. 32(4 + -4t + t2) = 0 Factor a trinomial. 32((2 + -1t)(2 + -1t)) = 0 Ignore the factor 32.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 '(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 = 2Solution
t = {2, 2}
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