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Simplifying -4.9t2 + 10t + 15 = 0 Reorder the terms: 15 + 10t + -4.9t2 = 0 Solving 15 + 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'. -3.06122449 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + -2.040816327t + 3.06122449 + t2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + -2.040816327t + t2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + -2.040816327t + t2 = 0 + 3.06122449 -2.040816327t + t2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 -2.040816327t + t2 = 3.06122449 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 = 3.06122449 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 3.06122449 + 1.041232821 Combine like terms: 3.06122449 + 1.041232821 = 4.102457311 1.041232821 + -2.040816327t + t2 = 4.102457311 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 4.102457311 Calculate the square root of the right side: 2.025452372 Break this problem into two subproblems by setting (t + -1.020408164) equal to 2.025452372 and -2.025452372.Subproblem 1
t + -1.020408164 = 2.025452372 Simplifying t + -1.020408164 = 2.025452372 Reorder the terms: -1.020408164 + t = 2.025452372 Solving -1.020408164 + t = 2.025452372 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 = 2.025452372 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 2.025452372 + 1.020408164 t = 2.025452372 + 1.020408164 Combine like terms: 2.025452372 + 1.020408164 = 3.045860536 t = 3.045860536 Simplifying t = 3.045860536Subproblem 2
t + -1.020408164 = -2.025452372 Simplifying t + -1.020408164 = -2.025452372 Reorder the terms: -1.020408164 + t = -2.025452372 Solving -1.020408164 + t = -2.025452372 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 = -2.025452372 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -2.025452372 + 1.020408164 t = -2.025452372 + 1.020408164 Combine like terms: -2.025452372 + 1.020408164 = -1.005044208 t = -1.005044208 Simplifying t = -1.005044208Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.045860536, -1.005044208}
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