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Simplifying 0.75 = 4.9t2 + 20t Reorder the terms: 0.75 = 20t + 4.9t2 Solving 0.75 = 20t + 4.9t2 Solving for variable 't'. Reorder the terms: 0.75 + -20t + -4.9t2 = 20t + -20t + 4.9t2 + -4.9t2 Combine like terms: 20t + -20t = 0 0.75 + -20t + -4.9t2 = 0 + 4.9t2 + -4.9t2 0.75 + -20t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 0.75 + -20t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.1530612245 + 4.081632653t + t2 = 0 Move the constant term to the right: Add '0.1530612245' to each side of the equation. -0.1530612245 + 4.081632653t + 0.1530612245 + t2 = 0 + 0.1530612245 Reorder the terms: -0.1530612245 + 0.1530612245 + 4.081632653t + t2 = 0 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + 4.081632653t + t2 = 0 + 0.1530612245 4.081632653t + t2 = 0 + 0.1530612245 Combine like terms: 0 + 0.1530612245 = 0.1530612245 4.081632653t + t2 = 0.1530612245 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 = 0.1530612245 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653t + t2 = 0.1530612245 + 4.164931281 Combine like terms: 0.1530612245 + 4.164931281 = 4.3179925055 4.164931281 + 4.081632653t + t2 = 4.3179925055 Factor a perfect square on the left side: (t + 2.040816327)(t + 2.040816327) = 4.3179925055 Calculate the square root of the right side: 2.077977985 Break this problem into two subproblems by setting (t + 2.040816327) equal to 2.077977985 and -2.077977985.Subproblem 1
t + 2.040816327 = 2.077977985 Simplifying t + 2.040816327 = 2.077977985 Reorder the terms: 2.040816327 + t = 2.077977985 Solving 2.040816327 + t = 2.077977985 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 = 2.077977985 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = 2.077977985 + -2.040816327 t = 2.077977985 + -2.040816327 Combine like terms: 2.077977985 + -2.040816327 = 0.037161658 t = 0.037161658 Simplifying t = 0.037161658Subproblem 2
t + 2.040816327 = -2.077977985 Simplifying t + 2.040816327 = -2.077977985 Reorder the terms: 2.040816327 + t = -2.077977985 Solving 2.040816327 + t = -2.077977985 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 = -2.077977985 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = -2.077977985 + -2.040816327 t = -2.077977985 + -2.040816327 Combine like terms: -2.077977985 + -2.040816327 = -4.118794312 t = -4.118794312 Simplifying t = -4.118794312Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.037161658, -4.118794312}
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