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Simplifying 0 = -4.9t2 + 10t + 300 Reorder the terms: 0 = 300 + 10t + -4.9t2 Solving 0 = 300 + 10t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -300 = -300 -300 + -10t + 4.9t2 = 300 + 10t + -4.9t2 + -300 + -10t + 4.9t2 Reorder the terms: -300 + -10t + 4.9t2 = 300 + -300 + 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: 300 + -300 = 0 -300 + -10t + 4.9t2 = 0 + 10t + -10t + -4.9t2 + 4.9t2 -300 + -10t + 4.9t2 = 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: 10t + -10t = 0 -300 + -10t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -300 + -10t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -300 + -10t + 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'. -61.2244898 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '61.2244898' to each side of the equation. -61.2244898 + -2.040816327t + 61.2244898 + t2 = 0 + 61.2244898 Reorder the terms: -61.2244898 + 61.2244898 + -2.040816327t + t2 = 0 + 61.2244898 Combine like terms: -61.2244898 + 61.2244898 = 0.0000000 0.0000000 + -2.040816327t + t2 = 0 + 61.2244898 -2.040816327t + t2 = 0 + 61.2244898 Combine like terms: 0 + 61.2244898 = 61.2244898 -2.040816327t + t2 = 61.2244898 The t term is -2.040816327t. Take half its coefficient (-1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. -2.040816327t + 1.041232821 + t2 = 61.2244898 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 61.2244898 + 1.041232821 Combine like terms: 61.2244898 + 1.041232821 = 62.265722621 1.041232821 + -2.040816327t + t2 = 62.265722621 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 62.265722621 Calculate the square root of the right side: 7.890863237 Break this problem into two subproblems by setting (t + -1.020408164) equal to 7.890863237 and -7.890863237.Subproblem 1
t + -1.020408164 = 7.890863237 Simplifying t + -1.020408164 = 7.890863237 Reorder the terms: -1.020408164 + t = 7.890863237 Solving -1.020408164 + t = 7.890863237 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = 7.890863237 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 7.890863237 + 1.020408164 t = 7.890863237 + 1.020408164 Combine like terms: 7.890863237 + 1.020408164 = 8.911271401 t = 8.911271401 Simplifying t = 8.911271401Subproblem 2
t + -1.020408164 = -7.890863237 Simplifying t + -1.020408164 = -7.890863237 Reorder the terms: -1.020408164 + t = -7.890863237 Solving -1.020408164 + t = -7.890863237 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = -7.890863237 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -7.890863237 + 1.020408164 t = -7.890863237 + 1.020408164 Combine like terms: -7.890863237 + 1.020408164 = -6.870455073 t = -6.870455073 Simplifying t = -6.870455073Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.911271401, -6.870455073}
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