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Simplifying 38 = 0.5t2 + 8t Reorder the terms: 38 = 8t + 0.5t2 Solving 38 = 8t + 0.5t2 Solving for variable 't'. Reorder the terms: 38 + -8t + -0.5t2 = 8t + -8t + 0.5t2 + -0.5t2 Combine like terms: 8t + -8t = 0 38 + -8t + -0.5t2 = 0 + 0.5t2 + -0.5t2 38 + -8t + -0.5t2 = 0.5t2 + -0.5t2 Combine like terms: 0.5t2 + -0.5t2 = 0.0 38 + -8t + -0.5t2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -76 + 16t + t2 = 0 Move the constant term to the right: Add '76' to each side of the equation. -76 + 16t + 76 + t2 = 0 + 76 Reorder the terms: -76 + 76 + 16t + t2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 16t + t2 = 0 + 76 16t + t2 = 0 + 76 Combine like terms: 0 + 76 = 76 16t + t2 = 76 The t term is 16t. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16t + 64 + t2 = 76 + 64 Reorder the terms: 64 + 16t + t2 = 76 + 64 Combine like terms: 76 + 64 = 140 64 + 16t + t2 = 140 Factor a perfect square on the left side: (t + 8)(t + 8) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (t + 8) equal to 11.832159566 and -11.832159566.Subproblem 1
t + 8 = 11.832159566 Simplifying t + 8 = 11.832159566 Reorder the terms: 8 + t = 11.832159566 Solving 8 + t = 11.832159566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = 11.832159566 + -8 Combine like terms: 8 + -8 = 0 0 + t = 11.832159566 + -8 t = 11.832159566 + -8 Combine like terms: 11.832159566 + -8 = 3.832159566 t = 3.832159566 Simplifying t = 3.832159566Subproblem 2
t + 8 = -11.832159566 Simplifying t + 8 = -11.832159566 Reorder the terms: 8 + t = -11.832159566 Solving 8 + t = -11.832159566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = -11.832159566 + -8 Combine like terms: 8 + -8 = 0 0 + t = -11.832159566 + -8 t = -11.832159566 + -8 Combine like terms: -11.832159566 + -8 = -19.832159566 t = -19.832159566 Simplifying t = -19.832159566Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.832159566, -19.832159566}
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