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Simplifying 4.9t2 + -19.8t + 15 = 0 Reorder the terms: 15 + -19.8t + 4.9t2 = 0 Solving 15 + -19.8t + 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'. 3.06122449 + -4.040816327t + t2 = 0 Move the constant term to the right: Add '-3.06122449' to each side of the equation. 3.06122449 + -4.040816327t + -3.06122449 + t2 = 0 + -3.06122449 Reorder the terms: 3.06122449 + -3.06122449 + -4.040816327t + t2 = 0 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + -4.040816327t + t2 = 0 + -3.06122449 -4.040816327t + t2 = 0 + -3.06122449 Combine like terms: 0 + -3.06122449 = -3.06122449 -4.040816327t + t2 = -3.06122449 The t term is -4.040816327t. Take half its coefficient (-2.020408164). Square it (4.082049149) and add it to both sides. Add '4.082049149' to each side of the equation. -4.040816327t + 4.082049149 + t2 = -3.06122449 + 4.082049149 Reorder the terms: 4.082049149 + -4.040816327t + t2 = -3.06122449 + 4.082049149 Combine like terms: -3.06122449 + 4.082049149 = 1.020824659 4.082049149 + -4.040816327t + t2 = 1.020824659 Factor a perfect square on the left side: (t + -2.020408164)(t + -2.020408164) = 1.020824659 Calculate the square root of the right side: 1.010358678 Break this problem into two subproblems by setting (t + -2.020408164) equal to 1.010358678 and -1.010358678.Subproblem 1
t + -2.020408164 = 1.010358678 Simplifying t + -2.020408164 = 1.010358678 Reorder the terms: -2.020408164 + t = 1.010358678 Solving -2.020408164 + t = 1.010358678 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.020408164' to each side of the equation. -2.020408164 + 2.020408164 + t = 1.010358678 + 2.020408164 Combine like terms: -2.020408164 + 2.020408164 = 0.000000000 0.000000000 + t = 1.010358678 + 2.020408164 t = 1.010358678 + 2.020408164 Combine like terms: 1.010358678 + 2.020408164 = 3.030766842 t = 3.030766842 Simplifying t = 3.030766842Subproblem 2
t + -2.020408164 = -1.010358678 Simplifying t + -2.020408164 = -1.010358678 Reorder the terms: -2.020408164 + t = -1.010358678 Solving -2.020408164 + t = -1.010358678 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.020408164' to each side of the equation. -2.020408164 + 2.020408164 + t = -1.010358678 + 2.020408164 Combine like terms: -2.020408164 + 2.020408164 = 0.000000000 0.000000000 + t = -1.010358678 + 2.020408164 t = -1.010358678 + 2.020408164 Combine like terms: -1.010358678 + 2.020408164 = 1.010049486 t = 1.010049486 Simplifying t = 1.010049486Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.030766842, 1.010049486}
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