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Simplifying 0 = -16t2 + -20t + 25 Reorder the terms: 0 = 25 + -20t + -16t2 Solving 0 = 25 + -20t + -16t2 Solving for variable 't'. Combine like terms: 0 + -25 = -25 -25 + 20t + 16t2 = 25 + -20t + -16t2 + -25 + 20t + 16t2 Reorder the terms: -25 + 20t + 16t2 = 25 + -25 + -20t + 20t + -16t2 + 16t2 Combine like terms: 25 + -25 = 0 -25 + 20t + 16t2 = 0 + -20t + 20t + -16t2 + 16t2 -25 + 20t + 16t2 = -20t + 20t + -16t2 + 16t2 Combine like terms: -20t + 20t = 0 -25 + 20t + 16t2 = 0 + -16t2 + 16t2 -25 + 20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -25 + 20t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + 1.25t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 1.25t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 1.25t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 1.25t + t2 = 0 + 1.5625 1.25t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 1.25t + t2 = 1.5625 The t term is 1.25t. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25t + 0.390625 + t2 = 1.5625 + 0.390625 Reorder the terms: 0.390625 + 1.25t + t2 = 1.5625 + 0.390625 Combine like terms: 1.5625 + 0.390625 = 1.953125 0.390625 + 1.25t + t2 = 1.953125 Factor a perfect square on the left side: (t + 0.625)(t + 0.625) = 1.953125 Calculate the square root of the right side: 1.397542486 Break this problem into two subproblems by setting (t + 0.625) equal to 1.397542486 and -1.397542486.Subproblem 1
t + 0.625 = 1.397542486 Simplifying t + 0.625 = 1.397542486 Reorder the terms: 0.625 + t = 1.397542486 Solving 0.625 + t = 1.397542486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + t = 1.397542486 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + t = 1.397542486 + -0.625 t = 1.397542486 + -0.625 Combine like terms: 1.397542486 + -0.625 = 0.772542486 t = 0.772542486 Simplifying t = 0.772542486Subproblem 2
t + 0.625 = -1.397542486 Simplifying t + 0.625 = -1.397542486 Reorder the terms: 0.625 + t = -1.397542486 Solving 0.625 + t = -1.397542486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + t = -1.397542486 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + t = -1.397542486 + -0.625 t = -1.397542486 + -0.625 Combine like terms: -1.397542486 + -0.625 = -2.022542486 t = -2.022542486 Simplifying t = -2.022542486Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.772542486, -2.022542486}
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