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Simplifying 0 = -16t2 + 5t + 400 Reorder the terms: 0 = 400 + 5t + -16t2 Solving 0 = 400 + 5t + -16t2 Solving for variable 't'. Combine like terms: 0 + -400 = -400 -400 + -5t + 16t2 = 400 + 5t + -16t2 + -400 + -5t + 16t2 Reorder the terms: -400 + -5t + 16t2 = 400 + -400 + 5t + -5t + -16t2 + 16t2 Combine like terms: 400 + -400 = 0 -400 + -5t + 16t2 = 0 + 5t + -5t + -16t2 + 16t2 -400 + -5t + 16t2 = 5t + -5t + -16t2 + 16t2 Combine like terms: 5t + -5t = 0 -400 + -5t + 16t2 = 0 + -16t2 + 16t2 -400 + -5t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -400 + -5t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -25 + -0.3125t + t2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -0.3125t + 25 + t2 = 0 + 25 Reorder the terms: -25 + 25 + -0.3125t + t2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -0.3125t + t2 = 0 + 25 -0.3125t + t2 = 0 + 25 Combine like terms: 0 + 25 = 25 -0.3125t + t2 = 25 The t term is -0.3125t. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125t + 0.0244140625 + t2 = 25 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125t + t2 = 25 + 0.0244140625 Combine like terms: 25 + 0.0244140625 = 25.0244140625 0.0244140625 + -0.3125t + t2 = 25.0244140625 Factor a perfect square on the left side: (t + -0.15625)(t + -0.15625) = 25.0244140625 Calculate the square root of the right side: 5.00244081 Break this problem into two subproblems by setting (t + -0.15625) equal to 5.00244081 and -5.00244081.Subproblem 1
t + -0.15625 = 5.00244081 Simplifying t + -0.15625 = 5.00244081 Reorder the terms: -0.15625 + t = 5.00244081 Solving -0.15625 + t = 5.00244081 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = 5.00244081 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = 5.00244081 + 0.15625 t = 5.00244081 + 0.15625 Combine like terms: 5.00244081 + 0.15625 = 5.15869081 t = 5.15869081 Simplifying t = 5.15869081Subproblem 2
t + -0.15625 = -5.00244081 Simplifying t + -0.15625 = -5.00244081 Reorder the terms: -0.15625 + t = -5.00244081 Solving -0.15625 + t = -5.00244081 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = -5.00244081 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = -5.00244081 + 0.15625 t = -5.00244081 + 0.15625 Combine like terms: -5.00244081 + 0.15625 = -4.84619081 t = -4.84619081 Simplifying t = -4.84619081Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.15869081, -4.84619081}
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