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Simplifying 4.9t2 + 20t + -5 = 0 Reorder the terms: -5 + 20t + 4.9t2 = 0 Solving -5 + 20t + 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'. -1.020408163 + 4.081632653t + t2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + 4.081632653t + 1.020408163 + t2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + 4.081632653t + t2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + 4.081632653t + t2 = 0 + 1.020408163 4.081632653t + t2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 4.081632653t + t2 = 1.020408163 The t term is 4.081632653t. Take half its coefficient (2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. 4.081632653t + 4.164931281 + t2 = 1.020408163 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653t + t2 = 1.020408163 + 4.164931281 Combine like terms: 1.020408163 + 4.164931281 = 5.185339444 4.164931281 + 4.081632653t + t2 = 5.185339444 Factor a perfect square on the left side: (t + 2.040816327)(t + 2.040816327) = 5.185339444 Calculate the square root of the right side: 2.277134042 Break this problem into two subproblems by setting (t + 2.040816327) equal to 2.277134042 and -2.277134042.Subproblem 1
t + 2.040816327 = 2.277134042 Simplifying t + 2.040816327 = 2.277134042 Reorder the terms: 2.040816327 + t = 2.277134042 Solving 2.040816327 + t = 2.277134042 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + t = 2.277134042 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = 2.277134042 + -2.040816327 t = 2.277134042 + -2.040816327 Combine like terms: 2.277134042 + -2.040816327 = 0.236317715 t = 0.236317715 Simplifying t = 0.236317715Subproblem 2
t + 2.040816327 = -2.277134042 Simplifying t + 2.040816327 = -2.277134042 Reorder the terms: 2.040816327 + t = -2.277134042 Solving 2.040816327 + t = -2.277134042 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + t = -2.277134042 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = -2.277134042 + -2.040816327 t = -2.277134042 + -2.040816327 Combine like terms: -2.277134042 + -2.040816327 = -4.317950369 t = -4.317950369 Simplifying t = -4.317950369Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.236317715, -4.317950369}
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