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Simplifying 50 = 10t + 4.9t2 Solving 50 = 10t + 4.9t2 Solving for variable 't'. Reorder the terms: 50 + -10t + -4.9t2 = 10t + -10t + 4.9t2 + -4.9t2 Combine like terms: 10t + -10t = 0 50 + -10t + -4.9t2 = 0 + 4.9t2 + -4.9t2 50 + -10t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 50 + -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'. -10.20408163 + 2.040816327t + t2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 2.040816327t + 10.20408163 + t2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 2.040816327t + t2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 2.040816327t + t2 = 0 + 10.20408163 2.040816327t + t2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 2.040816327t + t2 = 10.20408163 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 = 10.20408163 + 1.041232821 Reorder the terms: 1.041232821 + 2.040816327t + t2 = 10.20408163 + 1.041232821 Combine like terms: 10.20408163 + 1.041232821 = 11.245314451 1.041232821 + 2.040816327t + t2 = 11.245314451 Factor a perfect square on the left side: (t + 1.020408164)(t + 1.020408164) = 11.245314451 Calculate the square root of the right side: 3.353403413 Break this problem into two subproblems by setting (t + 1.020408164) equal to 3.353403413 and -3.353403413.Subproblem 1
t + 1.020408164 = 3.353403413 Simplifying t + 1.020408164 = 3.353403413 Reorder the terms: 1.020408164 + t = 3.353403413 Solving 1.020408164 + t = 3.353403413 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 = 3.353403413 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + t = 3.353403413 + -1.020408164 t = 3.353403413 + -1.020408164 Combine like terms: 3.353403413 + -1.020408164 = 2.332995249 t = 2.332995249 Simplifying t = 2.332995249Subproblem 2
t + 1.020408164 = -3.353403413 Simplifying t + 1.020408164 = -3.353403413 Reorder the terms: 1.020408164 + t = -3.353403413 Solving 1.020408164 + t = -3.353403413 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 = -3.353403413 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + t = -3.353403413 + -1.020408164 t = -3.353403413 + -1.020408164 Combine like terms: -3.353403413 + -1.020408164 = -4.373811577 t = -4.373811577 Simplifying t = -4.373811577Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.332995249, -4.373811577}
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