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Simplifying 0 = 4.9t2 + -80t + 96 Reorder the terms: 0 = 96 + -80t + 4.9t2 Solving 0 = 96 + -80t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + -96 = -96 -96 + 80t + -4.9t2 = 96 + -80t + 4.9t2 + -96 + 80t + -4.9t2 Reorder the terms: -96 + 80t + -4.9t2 = 96 + -96 + -80t + 80t + 4.9t2 + -4.9t2 Combine like terms: 96 + -96 = 0 -96 + 80t + -4.9t2 = 0 + -80t + 80t + 4.9t2 + -4.9t2 -96 + 80t + -4.9t2 = -80t + 80t + 4.9t2 + -4.9t2 Combine like terms: -80t + 80t = 0 -96 + 80t + -4.9t2 = 0 + 4.9t2 + -4.9t2 -96 + 80t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -96 + 80t + -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'. 19.59183673 + -16.32653061t + t2 = 0 Move the constant term to the right: Add '-19.59183673' to each side of the equation. 19.59183673 + -16.32653061t + -19.59183673 + t2 = 0 + -19.59183673 Reorder the terms: 19.59183673 + -19.59183673 + -16.32653061t + t2 = 0 + -19.59183673 Combine like terms: 19.59183673 + -19.59183673 = 0.00000000 0.00000000 + -16.32653061t + t2 = 0 + -19.59183673 -16.32653061t + t2 = 0 + -19.59183673 Combine like terms: 0 + -19.59183673 = -19.59183673 -16.32653061t + t2 = -19.59183673 The t term is -16.32653061t. Take half its coefficient (-8.163265305). Square it (66.63890044) and add it to both sides. Add '66.63890044' to each side of the equation. -16.32653061t + 66.63890044 + t2 = -19.59183673 + 66.63890044 Reorder the terms: 66.63890044 + -16.32653061t + t2 = -19.59183673 + 66.63890044 Combine like terms: -19.59183673 + 66.63890044 = 47.04706371 66.63890044 + -16.32653061t + t2 = 47.04706371 Factor a perfect square on the left side: (t + -8.163265305)(t + -8.163265305) = 47.04706371 Calculate the square root of the right side: 6.859086215 Break this problem into two subproblems by setting (t + -8.163265305) equal to 6.859086215 and -6.859086215.Subproblem 1
t + -8.163265305 = 6.859086215 Simplifying t + -8.163265305 = 6.859086215 Reorder the terms: -8.163265305 + t = 6.859086215 Solving -8.163265305 + t = 6.859086215 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.163265305' to each side of the equation. -8.163265305 + 8.163265305 + t = 6.859086215 + 8.163265305 Combine like terms: -8.163265305 + 8.163265305 = 0.000000000 0.000000000 + t = 6.859086215 + 8.163265305 t = 6.859086215 + 8.163265305 Combine like terms: 6.859086215 + 8.163265305 = 15.02235152 t = 15.02235152 Simplifying t = 15.02235152Subproblem 2
t + -8.163265305 = -6.859086215 Simplifying t + -8.163265305 = -6.859086215 Reorder the terms: -8.163265305 + t = -6.859086215 Solving -8.163265305 + t = -6.859086215 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.163265305' to each side of the equation. -8.163265305 + 8.163265305 + t = -6.859086215 + 8.163265305 Combine like terms: -8.163265305 + 8.163265305 = 0.000000000 0.000000000 + t = -6.859086215 + 8.163265305 t = -6.859086215 + 8.163265305 Combine like terms: -6.859086215 + 8.163265305 = 1.30417909 t = 1.30417909 Simplifying t = 1.30417909Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.02235152, 1.30417909}
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