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Simplifying t(7t + 21) = 490 Reorder the terms: t(21 + 7t) = 490 (21 * t + 7t * t) = 490 (21t + 7t2) = 490 Solving 21t + 7t2 = 490 Solving for variable 't'. Reorder the terms: -490 + 21t + 7t2 = 490 + -490 Combine like terms: 490 + -490 = 0 -490 + 21t + 7t2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-70 + 3t + t2) = 0 Factor a trinomial. 7((-10 + -1t)(7 + -1t)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-10 + -1t)' equal to zero and attempt to solve: Simplifying -10 + -1t = 0 Solving -10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1t = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1t = 0 + 10 -1t = 0 + 10 Combine like terms: 0 + 10 = 10 -1t = 10 Divide each side by '-1'. t = -10 Simplifying t = -10Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {-10, 7}
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