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Simplifying 0 = -490t2 + 1120t + -640 Reorder the terms: 0 = -640 + 1120t + -490t2 Solving 0 = -640 + 1120t + -490t2 Solving for variable 't'. Combine like terms: 0 + 640 = 640 640 + -1120t + 490t2 = -640 + 1120t + -490t2 + 640 + -1120t + 490t2 Reorder the terms: 640 + -1120t + 490t2 = -640 + 640 + 1120t + -1120t + -490t2 + 490t2 Combine like terms: -640 + 640 = 0 640 + -1120t + 490t2 = 0 + 1120t + -1120t + -490t2 + 490t2 640 + -1120t + 490t2 = 1120t + -1120t + -490t2 + 490t2 Combine like terms: 1120t + -1120t = 0 640 + -1120t + 490t2 = 0 + -490t2 + 490t2 640 + -1120t + 490t2 = -490t2 + 490t2 Combine like terms: -490t2 + 490t2 = 0 640 + -1120t + 490t2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(64 + -112t + 49t2) = 0 Factor a trinomial. 10((8 + -7t)(8 + -7t)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(8 + -7t)' equal to zero and attempt to solve: Simplifying 8 + -7t = 0 Solving 8 + -7t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7t = 0 + -8 -7t = 0 + -8 Combine like terms: 0 + -8 = -8 -7t = -8 Divide each side by '-7'. t = 1.142857143 Simplifying t = 1.142857143Subproblem 2
Set the factor '(8 + -7t)' equal to zero and attempt to solve: Simplifying 8 + -7t = 0 Solving 8 + -7t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7t = 0 + -8 -7t = 0 + -8 Combine like terms: 0 + -8 = -8 -7t = -8 Divide each side by '-7'. t = 1.142857143 Simplifying t = 1.142857143Solution
t = {1.142857143, 1.142857143}
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