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Simplifying 0 = -16t2 + 62t + 3 Reorder the terms: 0 = 3 + 62t + -16t2 Solving 0 = 3 + 62t + -16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -62t + 16t2 = 3 + 62t + -16t2 + -3 + -62t + 16t2 Reorder the terms: -3 + -62t + 16t2 = 3 + -3 + 62t + -62t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 -3 + -62t + 16t2 = 0 + 62t + -62t + -16t2 + 16t2 -3 + -62t + 16t2 = 62t + -62t + -16t2 + 16t2 Combine like terms: 62t + -62t = 0 -3 + -62t + 16t2 = 0 + -16t2 + 16t2 -3 + -62t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -3 + -62t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -3.875t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -3.875t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -3.875t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -3.875t + t2 = 0 + 0.1875 -3.875t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -3.875t + t2 = 0.1875 The t term is -3.875t. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875t + 3.75390625 + t2 = 0.1875 + 3.75390625 Reorder the terms: 3.75390625 + -3.875t + t2 = 0.1875 + 3.75390625 Combine like terms: 0.1875 + 3.75390625 = 3.94140625 3.75390625 + -3.875t + t2 = 3.94140625 Factor a perfect square on the left side: (t + -1.9375)(t + -1.9375) = 3.94140625 Calculate the square root of the right side: 1.985297522 Break this problem into two subproblems by setting (t + -1.9375) equal to 1.985297522 and -1.985297522.Subproblem 1
t + -1.9375 = 1.985297522 Simplifying t + -1.9375 = 1.985297522 Reorder the terms: -1.9375 + t = 1.985297522 Solving -1.9375 + t = 1.985297522 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = 1.985297522 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = 1.985297522 + 1.9375 t = 1.985297522 + 1.9375 Combine like terms: 1.985297522 + 1.9375 = 3.922797522 t = 3.922797522 Simplifying t = 3.922797522Subproblem 2
t + -1.9375 = -1.985297522 Simplifying t + -1.9375 = -1.985297522 Reorder the terms: -1.9375 + t = -1.985297522 Solving -1.9375 + t = -1.985297522 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = -1.985297522 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = -1.985297522 + 1.9375 t = -1.985297522 + 1.9375 Combine like terms: -1.985297522 + 1.9375 = -0.047797522 t = -0.047797522 Simplifying t = -0.047797522Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.922797522, -0.047797522}
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