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Simplifying 10 = 45t + -16t2 Solving 10 = 45t + -16t2 Solving for variable 't'. Reorder the terms: 10 + -45t + 16t2 = 45t + -45t + -16t2 + 16t2 Combine like terms: 45t + -45t = 0 10 + -45t + 16t2 = 0 + -16t2 + 16t2 10 + -45t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 10 + -45t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.625 + -2.8125t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -2.8125t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -2.8125t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -2.8125t + t2 = 0 + -0.625 -2.8125t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -2.8125t + t2 = -0.625 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 = -0.625 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = -0.625 + 1.977539063 Combine like terms: -0.625 + 1.977539063 = 1.352539063 1.977539063 + -2.8125t + t2 = 1.352539063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 1.352539063 Calculate the square root of the right side: 1.162987129 Break this problem into two subproblems by setting (t + -1.40625) equal to 1.162987129 and -1.162987129.Subproblem 1
t + -1.40625 = 1.162987129 Simplifying t + -1.40625 = 1.162987129 Reorder the terms: -1.40625 + t = 1.162987129 Solving -1.40625 + t = 1.162987129 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 = 1.162987129 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 1.162987129 + 1.40625 t = 1.162987129 + 1.40625 Combine like terms: 1.162987129 + 1.40625 = 2.569237129 t = 2.569237129 Simplifying t = 2.569237129Subproblem 2
t + -1.40625 = -1.162987129 Simplifying t + -1.40625 = -1.162987129 Reorder the terms: -1.40625 + t = -1.162987129 Solving -1.40625 + t = -1.162987129 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 = -1.162987129 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -1.162987129 + 1.40625 t = -1.162987129 + 1.40625 Combine like terms: -1.162987129 + 1.40625 = 0.243262871 t = 0.243262871 Simplifying t = 0.243262871Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.569237129, 0.243262871}
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