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Simplifying 850 = 8t + 4.9t2 Solving 850 = 8t + 4.9t2 Solving for variable 't'. Reorder the terms: 850 + -8t + -4.9t2 = 8t + -8t + 4.9t2 + -4.9t2 Combine like terms: 8t + -8t = 0 850 + -8t + -4.9t2 = 0 + 4.9t2 + -4.9t2 850 + -8t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 850 + -8t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -173.4693878 + 1.632653061t + t2 = 0 Move the constant term to the right: Add '173.4693878' to each side of the equation. -173.4693878 + 1.632653061t + 173.4693878 + t2 = 0 + 173.4693878 Reorder the terms: -173.4693878 + 173.4693878 + 1.632653061t + t2 = 0 + 173.4693878 Combine like terms: -173.4693878 + 173.4693878 = 0.0000000 0.0000000 + 1.632653061t + t2 = 0 + 173.4693878 1.632653061t + t2 = 0 + 173.4693878 Combine like terms: 0 + 173.4693878 = 173.4693878 1.632653061t + t2 = 173.4693878 The t term is 1.632653061t. Take half its coefficient (0.8163265305). Square it (0.6663890044) and add it to both sides. Add '0.6663890044' to each side of the equation. 1.632653061t + 0.6663890044 + t2 = 173.4693878 + 0.6663890044 Reorder the terms: 0.6663890044 + 1.632653061t + t2 = 173.4693878 + 0.6663890044 Combine like terms: 173.4693878 + 0.6663890044 = 174.1357768044 0.6663890044 + 1.632653061t + t2 = 174.1357768044 Factor a perfect square on the left side: (t + 0.8163265305)(t + 0.8163265305) = 174.1357768044 Calculate the square root of the right side: 13.196051561 Break this problem into two subproblems by setting (t + 0.8163265305) equal to 13.196051561 and -13.196051561.Subproblem 1
t + 0.8163265305 = 13.196051561 Simplifying t + 0.8163265305 = 13.196051561 Reorder the terms: 0.8163265305 + t = 13.196051561 Solving 0.8163265305 + t = 13.196051561 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8163265305' to each side of the equation. 0.8163265305 + -0.8163265305 + t = 13.196051561 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + t = 13.196051561 + -0.8163265305 t = 13.196051561 + -0.8163265305 Combine like terms: 13.196051561 + -0.8163265305 = 12.3797250305 t = 12.3797250305 Simplifying t = 12.3797250305Subproblem 2
t + 0.8163265305 = -13.196051561 Simplifying t + 0.8163265305 = -13.196051561 Reorder the terms: 0.8163265305 + t = -13.196051561 Solving 0.8163265305 + t = -13.196051561 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8163265305' to each side of the equation. 0.8163265305 + -0.8163265305 + t = -13.196051561 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + t = -13.196051561 + -0.8163265305 t = -13.196051561 + -0.8163265305 Combine like terms: -13.196051561 + -0.8163265305 = -14.0123780915 t = -14.0123780915 Simplifying t = -14.0123780915Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.3797250305, -14.0123780915}
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