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Simplifying 0 = -16t2 + 25t + 220 Reorder the terms: 0 = 220 + 25t + -16t2 Solving 0 = 220 + 25t + -16t2 Solving for variable 't'. Combine like terms: 0 + -220 = -220 -220 + -25t + 16t2 = 220 + 25t + -16t2 + -220 + -25t + 16t2 Reorder the terms: -220 + -25t + 16t2 = 220 + -220 + 25t + -25t + -16t2 + 16t2 Combine like terms: 220 + -220 = 0 -220 + -25t + 16t2 = 0 + 25t + -25t + -16t2 + 16t2 -220 + -25t + 16t2 = 25t + -25t + -16t2 + 16t2 Combine like terms: 25t + -25t = 0 -220 + -25t + 16t2 = 0 + -16t2 + 16t2 -220 + -25t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -220 + -25t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -13.75 + -1.5625t + t2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + -1.5625t + 13.75 + t2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + -1.5625t + t2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + -1.5625t + t2 = 0 + 13.75 -1.5625t + t2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 -1.5625t + t2 = 13.75 The t term is -1.5625t. Take half its coefficient (-0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. -1.5625t + 0.6103515625 + t2 = 13.75 + 0.6103515625 Reorder the terms: 0.6103515625 + -1.5625t + t2 = 13.75 + 0.6103515625 Combine like terms: 13.75 + 0.6103515625 = 14.3603515625 0.6103515625 + -1.5625t + t2 = 14.3603515625 Factor a perfect square on the left side: (t + -0.78125)(t + -0.78125) = 14.3603515625 Calculate the square root of the right side: 3.789505451 Break this problem into two subproblems by setting (t + -0.78125) equal to 3.789505451 and -3.789505451.Subproblem 1
t + -0.78125 = 3.789505451 Simplifying t + -0.78125 = 3.789505451 Reorder the terms: -0.78125 + t = 3.789505451 Solving -0.78125 + t = 3.789505451 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = 3.789505451 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = 3.789505451 + 0.78125 t = 3.789505451 + 0.78125 Combine like terms: 3.789505451 + 0.78125 = 4.570755451 t = 4.570755451 Simplifying t = 4.570755451Subproblem 2
t + -0.78125 = -3.789505451 Simplifying t + -0.78125 = -3.789505451 Reorder the terms: -0.78125 + t = -3.789505451 Solving -0.78125 + t = -3.789505451 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = -3.789505451 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = -3.789505451 + 0.78125 t = -3.789505451 + 0.78125 Combine like terms: -3.789505451 + 0.78125 = -3.008255451 t = -3.008255451 Simplifying t = -3.008255451Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.570755451, -3.008255451}
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