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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 = 4.0118700565 4.164931281 + -4.081632653t + t2 = 4.0118700565 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 4.0118700565 Calculate the square root of the right side: 2.002965316 Break this problem into two subproblems by setting (t + -2.040816327) equal to 2.002965316 and -2.002965316.Subproblem 1
t + -2.040816327 = 2.002965316 Simplifying t + -2.040816327 = 2.002965316 Reorder the terms: -2.040816327 + t = 2.002965316 Solving -2.040816327 + t = 2.002965316 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 = 2.002965316 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 2.002965316 + 2.040816327 t = 2.002965316 + 2.040816327 Combine like terms: 2.002965316 + 2.040816327 = 4.043781643 t = 4.043781643 Simplifying t = 4.043781643Subproblem 2
t + -2.040816327 = -2.002965316 Simplifying t + -2.040816327 = -2.002965316 Reorder the terms: -2.040816327 + t = -2.002965316 Solving -2.040816327 + t = -2.002965316 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 = -2.002965316 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -2.002965316 + 2.040816327 t = -2.002965316 + 2.040816327 Combine like terms: -2.002965316 + 2.040816327 = 0.037851011 t = 0.037851011 Simplifying t = 0.037851011Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.043781643, 0.037851011}
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