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Simplifying 0 = 16t2 + 63t + 4 Reorder the terms: 0 = 4 + 63t + 16t2 Solving 0 = 4 + 63t + 16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -63t + -16t2 = 4 + 63t + 16t2 + -4 + -63t + -16t2 Reorder the terms: -4 + -63t + -16t2 = 4 + -4 + 63t + -63t + 16t2 + -16t2 Combine like terms: 4 + -4 = 0 -4 + -63t + -16t2 = 0 + 63t + -63t + 16t2 + -16t2 -4 + -63t + -16t2 = 63t + -63t + 16t2 + -16t2 Combine like terms: 63t + -63t = 0 -4 + -63t + -16t2 = 0 + 16t2 + -16t2 -4 + -63t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -4 + -63t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 63t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 63t + 16t2)' equal to zero and attempt to solve: Simplifying 4 + 63t + 16t2 = 0 Solving 4 + 63t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.25 + 3.9375t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 3.9375t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 3.9375t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 3.9375t + t2 = 0 + -0.25 3.9375t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 3.9375t + t2 = -0.25 The t term is 3.9375t. Take half its coefficient (1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. 3.9375t + 3.875976563 + t2 = -0.25 + 3.875976563 Reorder the terms: 3.875976563 + 3.9375t + t2 = -0.25 + 3.875976563 Combine like terms: -0.25 + 3.875976563 = 3.625976563 3.875976563 + 3.9375t + t2 = 3.625976563 Factor a perfect square on the left side: (t + 1.96875)(t + 1.96875) = 3.625976563 Calculate the square root of the right side: 1.904199717 Break this problem into two subproblems by setting (t + 1.96875) equal to 1.904199717 and -1.904199717.Subproblem 1
t + 1.96875 = 1.904199717 Simplifying t + 1.96875 = 1.904199717 Reorder the terms: 1.96875 + t = 1.904199717 Solving 1.96875 + t = 1.904199717 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.96875' to each side of the equation. 1.96875 + -1.96875 + t = 1.904199717 + -1.96875 Combine like terms: 1.96875 + -1.96875 = 0.00000 0.00000 + t = 1.904199717 + -1.96875 t = 1.904199717 + -1.96875 Combine like terms: 1.904199717 + -1.96875 = -0.064550283 t = -0.064550283 Simplifying t = -0.064550283Subproblem 2
t + 1.96875 = -1.904199717 Simplifying t + 1.96875 = -1.904199717 Reorder the terms: 1.96875 + t = -1.904199717 Solving 1.96875 + t = -1.904199717 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.96875' to each side of the equation. 1.96875 + -1.96875 + t = -1.904199717 + -1.96875 Combine like terms: 1.96875 + -1.96875 = 0.00000 0.00000 + t = -1.904199717 + -1.96875 t = -1.904199717 + -1.96875 Combine like terms: -1.904199717 + -1.96875 = -3.872949717 t = -3.872949717 Simplifying t = -3.872949717Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.064550283, -3.872949717}Solution
t = {-0.064550283, -3.872949717}
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