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Simplifying 0 = -16t2 + 90t + 575 Reorder the terms: 0 = 575 + 90t + -16t2 Solving 0 = 575 + 90t + -16t2 Solving for variable 't'. Combine like terms: 0 + -575 = -575 -575 + -90t + 16t2 = 575 + 90t + -16t2 + -575 + -90t + 16t2 Reorder the terms: -575 + -90t + 16t2 = 575 + -575 + 90t + -90t + -16t2 + 16t2 Combine like terms: 575 + -575 = 0 -575 + -90t + 16t2 = 0 + 90t + -90t + -16t2 + 16t2 -575 + -90t + 16t2 = 90t + -90t + -16t2 + 16t2 Combine like terms: 90t + -90t = 0 -575 + -90t + 16t2 = 0 + -16t2 + 16t2 -575 + -90t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -575 + -90t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -35.9375 + -5.625t + t2 = 0 Move the constant term to the right: Add '35.9375' to each side of the equation. -35.9375 + -5.625t + 35.9375 + t2 = 0 + 35.9375 Reorder the terms: -35.9375 + 35.9375 + -5.625t + t2 = 0 + 35.9375 Combine like terms: -35.9375 + 35.9375 = 0.0000 0.0000 + -5.625t + t2 = 0 + 35.9375 -5.625t + t2 = 0 + 35.9375 Combine like terms: 0 + 35.9375 = 35.9375 -5.625t + t2 = 35.9375 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 = 35.9375 + 7.91015625 Reorder the terms: 7.91015625 + -5.625t + t2 = 35.9375 + 7.91015625 Combine like terms: 35.9375 + 7.91015625 = 43.84765625 7.91015625 + -5.625t + t2 = 43.84765625 Factor a perfect square on the left side: (t + -2.8125)(t + -2.8125) = 43.84765625 Calculate the square root of the right side: 6.621756281 Break this problem into two subproblems by setting (t + -2.8125) equal to 6.621756281 and -6.621756281.Subproblem 1
t + -2.8125 = 6.621756281 Simplifying t + -2.8125 = 6.621756281 Reorder the terms: -2.8125 + t = 6.621756281 Solving -2.8125 + t = 6.621756281 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 = 6.621756281 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = 6.621756281 + 2.8125 t = 6.621756281 + 2.8125 Combine like terms: 6.621756281 + 2.8125 = 9.434256281 t = 9.434256281 Simplifying t = 9.434256281Subproblem 2
t + -2.8125 = -6.621756281 Simplifying t + -2.8125 = -6.621756281 Reorder the terms: -2.8125 + t = -6.621756281 Solving -2.8125 + t = -6.621756281 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 = -6.621756281 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = -6.621756281 + 2.8125 t = -6.621756281 + 2.8125 Combine like terms: -6.621756281 + 2.8125 = -3.809256281 t = -3.809256281 Simplifying t = -3.809256281Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.434256281, -3.809256281}
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