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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 = 3.144523118 4.164931281 + -4.081632653t + t2 = 3.144523118 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 3.144523118 Calculate the square root of the right side: 1.773280327 Break this problem into two subproblems by setting (t + -2.040816327) equal to 1.773280327 and -1.773280327.Subproblem 1
t + -2.040816327 = 1.773280327 Simplifying t + -2.040816327 = 1.773280327 Reorder the terms: -2.040816327 + t = 1.773280327 Solving -2.040816327 + t = 1.773280327 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 = 1.773280327 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 1.773280327 + 2.040816327 t = 1.773280327 + 2.040816327 Combine like terms: 1.773280327 + 2.040816327 = 3.814096654 t = 3.814096654 Simplifying t = 3.814096654Subproblem 2
t + -2.040816327 = -1.773280327 Simplifying t + -2.040816327 = -1.773280327 Reorder the terms: -2.040816327 + t = -1.773280327 Solving -2.040816327 + t = -1.773280327 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 = -1.773280327 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -1.773280327 + 2.040816327 t = -1.773280327 + 2.040816327 Combine like terms: -1.773280327 + 2.040816327 = 0.267536 t = 0.267536 Simplifying t = 0.267536Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.814096654, 0.267536}
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