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Simplifying 15t2 + -56t + 15 = 0 Reorder the terms: 15 + -56t + 15t2 = 0 Solving 15 + -56t + 15t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1 + -3.733333333t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.733333333t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -3.733333333t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.733333333t + t2 = 0 + -1 -3.733333333t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.733333333t + t2 = -1 The t term is -3.733333333t. Take half its coefficient (-1.866666667). Square it (3.484444446) and add it to both sides. Add '3.484444446' to each side of the equation. -3.733333333t + 3.484444446 + t2 = -1 + 3.484444446 Reorder the terms: 3.484444446 + -3.733333333t + t2 = -1 + 3.484444446 Combine like terms: -1 + 3.484444446 = 2.484444446 3.484444446 + -3.733333333t + t2 = 2.484444446 Factor a perfect square on the left side: (t + -1.866666667)(t + -1.866666667) = 2.484444446 Calculate the square root of the right side: 1.576212056 Break this problem into two subproblems by setting (t + -1.866666667) equal to 1.576212056 and -1.576212056.Subproblem 1
t + -1.866666667 = 1.576212056 Simplifying t + -1.866666667 = 1.576212056 Reorder the terms: -1.866666667 + t = 1.576212056 Solving -1.866666667 + t = 1.576212056 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.866666667' to each side of the equation. -1.866666667 + 1.866666667 + t = 1.576212056 + 1.866666667 Combine like terms: -1.866666667 + 1.866666667 = 0.000000000 0.000000000 + t = 1.576212056 + 1.866666667 t = 1.576212056 + 1.866666667 Combine like terms: 1.576212056 + 1.866666667 = 3.442878723 t = 3.442878723 Simplifying t = 3.442878723Subproblem 2
t + -1.866666667 = -1.576212056 Simplifying t + -1.866666667 = -1.576212056 Reorder the terms: -1.866666667 + t = -1.576212056 Solving -1.866666667 + t = -1.576212056 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.866666667' to each side of the equation. -1.866666667 + 1.866666667 + t = -1.576212056 + 1.866666667 Combine like terms: -1.866666667 + 1.866666667 = 0.000000000 0.000000000 + t = -1.576212056 + 1.866666667 t = -1.576212056 + 1.866666667 Combine like terms: -1.576212056 + 1.866666667 = 0.290454611 t = 0.290454611 Simplifying t = 0.290454611Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.442878723, 0.290454611}
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