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Simplifying 0 = -16t2 + 90t + 5 Reorder the terms: 0 = 5 + 90t + -16t2 Solving 0 = 5 + 90t + -16t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -90t + 16t2 = 5 + 90t + -16t2 + -5 + -90t + 16t2 Reorder the terms: -5 + -90t + 16t2 = 5 + -5 + 90t + -90t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 -5 + -90t + 16t2 = 0 + 90t + -90t + -16t2 + 16t2 -5 + -90t + 16t2 = 90t + -90t + -16t2 + 16t2 Combine like terms: 90t + -90t = 0 -5 + -90t + 16t2 = 0 + -16t2 + 16t2 -5 + -90t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5 + -90t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -5.625t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -5.625t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -5.625t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -5.625t + t2 = 0 + 0.3125 -5.625t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -5.625t + t2 = 0.3125 The t term is -5.625t. Take half its coefficient (-2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. -5.625t + 7.91015625 + t2 = 0.3125 + 7.91015625 Reorder the terms: 7.91015625 + -5.625t + t2 = 0.3125 + 7.91015625 Combine like terms: 0.3125 + 7.91015625 = 8.22265625 7.91015625 + -5.625t + t2 = 8.22265625 Factor a perfect square on the left side: (t + -2.8125)(t + -2.8125) = 8.22265625 Calculate the square root of the right side: 2.867517437 Break this problem into two subproblems by setting (t + -2.8125) equal to 2.867517437 and -2.867517437.Subproblem 1
t + -2.8125 = 2.867517437 Simplifying t + -2.8125 = 2.867517437 Reorder the terms: -2.8125 + t = 2.867517437 Solving -2.8125 + t = 2.867517437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + t = 2.867517437 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = 2.867517437 + 2.8125 t = 2.867517437 + 2.8125 Combine like terms: 2.867517437 + 2.8125 = 5.680017437 t = 5.680017437 Simplifying t = 5.680017437Subproblem 2
t + -2.8125 = -2.867517437 Simplifying t + -2.8125 = -2.867517437 Reorder the terms: -2.8125 + t = -2.867517437 Solving -2.8125 + t = -2.867517437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + t = -2.867517437 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = -2.867517437 + 2.8125 t = -2.867517437 + 2.8125 Combine like terms: -2.867517437 + 2.8125 = -0.055017437 t = -0.055017437 Simplifying t = -0.055017437Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.680017437, -0.055017437}
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