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Simplifying -4.9t2 + 10t + 20 = 0 Reorder the terms: 20 + 10t + -4.9t2 = 0 Solving 20 + 10t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -4.081632653 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + -2.040816327t + 4.081632653 + t2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + -2.040816327t + t2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + -2.040816327t + t2 = 0 + 4.081632653 -2.040816327t + t2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 -2.040816327t + t2 = 4.081632653 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 = 4.081632653 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 4.081632653 + 1.041232821 Combine like terms: 4.081632653 + 1.041232821 = 5.122865474 1.041232821 + -2.040816327t + t2 = 5.122865474 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 5.122865474 Calculate the square root of the right side: 2.263374798 Break this problem into two subproblems by setting (t + -1.020408164) equal to 2.263374798 and -2.263374798.Subproblem 1
t + -1.020408164 = 2.263374798 Simplifying t + -1.020408164 = 2.263374798 Reorder the terms: -1.020408164 + t = 2.263374798 Solving -1.020408164 + t = 2.263374798 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 = 2.263374798 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 2.263374798 + 1.020408164 t = 2.263374798 + 1.020408164 Combine like terms: 2.263374798 + 1.020408164 = 3.283782962 t = 3.283782962 Simplifying t = 3.283782962Subproblem 2
t + -1.020408164 = -2.263374798 Simplifying t + -1.020408164 = -2.263374798 Reorder the terms: -1.020408164 + t = -2.263374798 Solving -1.020408164 + t = -2.263374798 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 = -2.263374798 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -2.263374798 + 1.020408164 t = -2.263374798 + 1.020408164 Combine like terms: -2.263374798 + 1.020408164 = -1.242966634 t = -1.242966634 Simplifying t = -1.242966634Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.283782962, -1.242966634}
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