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Simplifying -4.9t2 + 38t + -25 = 0 Reorder the terms: -25 + 38t + -4.9t2 = 0 Solving -25 + 38t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 5.102040816 + -7.755102041t + t2 = 0 Move the constant term to the right: Add '-5.102040816' to each side of the equation. 5.102040816 + -7.755102041t + -5.102040816 + t2 = 0 + -5.102040816 Reorder the terms: 5.102040816 + -5.102040816 + -7.755102041t + t2 = 0 + -5.102040816 Combine like terms: 5.102040816 + -5.102040816 = 0.000000000 0.000000000 + -7.755102041t + t2 = 0 + -5.102040816 -7.755102041t + t2 = 0 + -5.102040816 Combine like terms: 0 + -5.102040816 = -5.102040816 -7.755102041t + t2 = -5.102040816 The t term is -7.755102041t. Take half its coefficient (-3.877551021). Square it (15.03540192) and add it to both sides. Add '15.03540192' to each side of the equation. -7.755102041t + 15.03540192 + t2 = -5.102040816 + 15.03540192 Reorder the terms: 15.03540192 + -7.755102041t + t2 = -5.102040816 + 15.03540192 Combine like terms: -5.102040816 + 15.03540192 = 9.933361104 15.03540192 + -7.755102041t + t2 = 9.933361104 Factor a perfect square on the left side: (t + -3.877551021)(t + -3.877551021) = 9.933361104 Calculate the square root of the right side: 3.151723513 Break this problem into two subproblems by setting (t + -3.877551021) equal to 3.151723513 and -3.151723513.Subproblem 1
t + -3.877551021 = 3.151723513 Simplifying t + -3.877551021 = 3.151723513 Reorder the terms: -3.877551021 + t = 3.151723513 Solving -3.877551021 + t = 3.151723513 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.877551021' to each side of the equation. -3.877551021 + 3.877551021 + t = 3.151723513 + 3.877551021 Combine like terms: -3.877551021 + 3.877551021 = 0.000000000 0.000000000 + t = 3.151723513 + 3.877551021 t = 3.151723513 + 3.877551021 Combine like terms: 3.151723513 + 3.877551021 = 7.029274534 t = 7.029274534 Simplifying t = 7.029274534Subproblem 2
t + -3.877551021 = -3.151723513 Simplifying t + -3.877551021 = -3.151723513 Reorder the terms: -3.877551021 + t = -3.151723513 Solving -3.877551021 + t = -3.151723513 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.877551021' to each side of the equation. -3.877551021 + 3.877551021 + t = -3.151723513 + 3.877551021 Combine like terms: -3.877551021 + 3.877551021 = 0.000000000 0.000000000 + t = -3.151723513 + 3.877551021 t = -3.151723513 + 3.877551021 Combine like terms: -3.151723513 + 3.877551021 = 0.725827508 t = 0.725827508 Simplifying t = 0.725827508Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.029274534, 0.725827508}
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