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Simplifying 100 = -16t2 + 45t + 200 Reorder the terms: 100 = 200 + 45t + -16t2 Solving 100 = 200 + 45t + -16t2 Solving for variable 't'. Combine like terms: 100 + -200 = -100 -100 + -45t + 16t2 = 200 + 45t + -16t2 + -200 + -45t + 16t2 Reorder the terms: -100 + -45t + 16t2 = 200 + -200 + 45t + -45t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -100 + -45t + 16t2 = 0 + 45t + -45t + -16t2 + 16t2 -100 + -45t + 16t2 = 45t + -45t + -16t2 + 16t2 Combine like terms: 45t + -45t = 0 -100 + -45t + 16t2 = 0 + -16t2 + 16t2 -100 + -45t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + -45t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.25 + -2.8125t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -2.8125t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -2.8125t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -2.8125t + t2 = 0 + 6.25 -2.8125t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -2.8125t + t2 = 6.25 The t term is -2.8125t. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125t + 1.977539063 + t2 = 6.25 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = 6.25 + 1.977539063 Combine like terms: 6.25 + 1.977539063 = 8.227539063 1.977539063 + -2.8125t + t2 = 8.227539063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 8.227539063 Calculate the square root of the right side: 2.868368711 Break this problem into two subproblems by setting (t + -1.40625) equal to 2.868368711 and -2.868368711.Subproblem 1
t + -1.40625 = 2.868368711 Simplifying t + -1.40625 = 2.868368711 Reorder the terms: -1.40625 + t = 2.868368711 Solving -1.40625 + t = 2.868368711 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = 2.868368711 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 2.868368711 + 1.40625 t = 2.868368711 + 1.40625 Combine like terms: 2.868368711 + 1.40625 = 4.274618711 t = 4.274618711 Simplifying t = 4.274618711Subproblem 2
t + -1.40625 = -2.868368711 Simplifying t + -1.40625 = -2.868368711 Reorder the terms: -1.40625 + t = -2.868368711 Solving -1.40625 + t = -2.868368711 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = -2.868368711 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -2.868368711 + 1.40625 t = -2.868368711 + 1.40625 Combine like terms: -2.868368711 + 1.40625 = -1.462118711 t = -1.462118711 Simplifying t = -1.462118711Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.274618711, -1.462118711}
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