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Simplifying 9 = 1.5t + 4.9t2 Solving 9 = 1.5t + 4.9t2 Solving for variable 't'. Reorder the terms: 9 + -1.5t + -4.9t2 = 1.5t + -1.5t + 4.9t2 + -4.9t2 Combine like terms: 1.5t + -1.5t = 0.0 9 + -1.5t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2 9 + -1.5t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 9 + -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'. -1.836734694 + 0.306122449t + t2 = 0 Move the constant term to the right: Add '1.836734694' to each side of the equation. -1.836734694 + 0.306122449t + 1.836734694 + t2 = 0 + 1.836734694 Reorder the terms: -1.836734694 + 1.836734694 + 0.306122449t + t2 = 0 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + 0.306122449t + t2 = 0 + 1.836734694 0.306122449t + t2 = 0 + 1.836734694 Combine like terms: 0 + 1.836734694 = 1.836734694 0.306122449t + t2 = 1.836734694 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 = 1.836734694 + 0.02342773845 Reorder the terms: 0.02342773845 + 0.306122449t + t2 = 1.836734694 + 0.02342773845 Combine like terms: 1.836734694 + 0.02342773845 = 1.86016243245 0.02342773845 + 0.306122449t + t2 = 1.86016243245 Factor a perfect square on the left side: (t + 0.1530612245)(t + 0.1530612245) = 1.86016243245 Calculate the square root of the right side: 1.363877719 Break this problem into two subproblems by setting (t + 0.1530612245) equal to 1.363877719 and -1.363877719.Subproblem 1
t + 0.1530612245 = 1.363877719 Simplifying t + 0.1530612245 = 1.363877719 Reorder the terms: 0.1530612245 + t = 1.363877719 Solving 0.1530612245 + t = 1.363877719 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 = 1.363877719 + -0.1530612245 Combine like terms: 0.1530612245 + -0.1530612245 = 0.0000000000 0.0000000000 + t = 1.363877719 + -0.1530612245 t = 1.363877719 + -0.1530612245 Combine like terms: 1.363877719 + -0.1530612245 = 1.2108164945 t = 1.2108164945 Simplifying t = 1.2108164945Subproblem 2
t + 0.1530612245 = -1.363877719 Simplifying t + 0.1530612245 = -1.363877719 Reorder the terms: 0.1530612245 + t = -1.363877719 Solving 0.1530612245 + t = -1.363877719 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 = -1.363877719 + -0.1530612245 Combine like terms: 0.1530612245 + -0.1530612245 = 0.0000000000 0.0000000000 + t = -1.363877719 + -0.1530612245 t = -1.363877719 + -0.1530612245 Combine like terms: -1.363877719 + -0.1530612245 = -1.5169389435 t = -1.5169389435 Simplifying t = -1.5169389435Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.2108164945, -1.5169389435}
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