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Simplifying 3 = -4.9t2 + 1.5t + 17 Reorder the terms: 3 = 17 + 1.5t + -4.9t2 Solving 3 = 17 + 1.5t + -4.9t2 Solving for variable 't'. Combine like terms: 3 + -17 = -14 -14 + -1.5t + 4.9t2 = 17 + 1.5t + -4.9t2 + -17 + -1.5t + 4.9t2 Reorder the terms: -14 + -1.5t + 4.9t2 = 17 + -17 + 1.5t + -1.5t + -4.9t2 + 4.9t2 Combine like terms: 17 + -17 = 0 -14 + -1.5t + 4.9t2 = 0 + 1.5t + -1.5t + -4.9t2 + 4.9t2 -14 + -1.5t + 4.9t2 = 1.5t + -1.5t + -4.9t2 + 4.9t2 Combine like terms: 1.5t + -1.5t = 0.0 -14 + -1.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -14 + -1.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -14 + -1.5t + 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'. -2.857142857 + -0.306122449t + t2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -0.306122449t + 2.857142857 + t2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -0.306122449t + t2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -0.306122449t + t2 = 0 + 2.857142857 -0.306122449t + t2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -0.306122449t + t2 = 2.857142857 The t term is -0.306122449t. Take half its coefficient (-0.1530612245). Square it (0.02342773845) and add it to both sides. Add '0.02342773845' to each side of the equation. -0.306122449t + 0.02342773845 + t2 = 2.857142857 + 0.02342773845 Reorder the terms: 0.02342773845 + -0.306122449t + t2 = 2.857142857 + 0.02342773845 Combine like terms: 2.857142857 + 0.02342773845 = 2.88057059545 0.02342773845 + -0.306122449t + t2 = 2.88057059545 Factor a perfect square on the left side: (t + -0.1530612245)(t + -0.1530612245) = 2.88057059545 Calculate the square root of the right side: 1.69722438 Break this problem into two subproblems by setting (t + -0.1530612245) equal to 1.69722438 and -1.69722438.Subproblem 1
t + -0.1530612245 = 1.69722438 Simplifying t + -0.1530612245 = 1.69722438 Reorder the terms: -0.1530612245 + t = 1.69722438 Solving -0.1530612245 + t = 1.69722438 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1530612245' to each side of the equation. -0.1530612245 + 0.1530612245 + t = 1.69722438 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + t = 1.69722438 + 0.1530612245 t = 1.69722438 + 0.1530612245 Combine like terms: 1.69722438 + 0.1530612245 = 1.8502856045 t = 1.8502856045 Simplifying t = 1.8502856045Subproblem 2
t + -0.1530612245 = -1.69722438 Simplifying t + -0.1530612245 = -1.69722438 Reorder the terms: -0.1530612245 + t = -1.69722438 Solving -0.1530612245 + t = -1.69722438 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1530612245' to each side of the equation. -0.1530612245 + 0.1530612245 + t = -1.69722438 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + t = -1.69722438 + 0.1530612245 t = -1.69722438 + 0.1530612245 Combine like terms: -1.69722438 + 0.1530612245 = -1.5441631555 t = -1.5441631555 Simplifying t = -1.5441631555Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.8502856045, -1.5441631555}
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