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Simplifying -4.9t2 + 10t + 25 = 0 Reorder the terms: 25 + 10t + -4.9t2 = 0 Solving 25 + 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'. -5.102040816 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '5.102040816' to each side of the equation. -5.102040816 + -2.040816327t + 5.102040816 + t2 = 0 + 5.102040816 Reorder the terms: -5.102040816 + 5.102040816 + -2.040816327t + t2 = 0 + 5.102040816 Combine like terms: -5.102040816 + 5.102040816 = 0.000000000 0.000000000 + -2.040816327t + t2 = 0 + 5.102040816 -2.040816327t + t2 = 0 + 5.102040816 Combine like terms: 0 + 5.102040816 = 5.102040816 -2.040816327t + t2 = 5.102040816 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 = 5.102040816 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 5.102040816 + 1.041232821 Combine like terms: 5.102040816 + 1.041232821 = 6.143273637 1.041232821 + -2.040816327t + t2 = 6.143273637 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 6.143273637 Calculate the square root of the right side: 2.478562817 Break this problem into two subproblems by setting (t + -1.020408164) equal to 2.478562817 and -2.478562817.Subproblem 1
t + -1.020408164 = 2.478562817 Simplifying t + -1.020408164 = 2.478562817 Reorder the terms: -1.020408164 + t = 2.478562817 Solving -1.020408164 + t = 2.478562817 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 = 2.478562817 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 2.478562817 + 1.020408164 t = 2.478562817 + 1.020408164 Combine like terms: 2.478562817 + 1.020408164 = 3.498970981 t = 3.498970981 Simplifying t = 3.498970981Subproblem 2
t + -1.020408164 = -2.478562817 Simplifying t + -1.020408164 = -2.478562817 Reorder the terms: -1.020408164 + t = -2.478562817 Solving -1.020408164 + t = -2.478562817 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 = -2.478562817 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -2.478562817 + 1.020408164 t = -2.478562817 + 1.020408164 Combine like terms: -2.478562817 + 1.020408164 = -1.458154653 t = -1.458154653 Simplifying t = -1.458154653Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.498970981, -1.458154653}
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