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Simplifying 4.9t2 + 2.5t + -9 = 0 Reorder the terms: -9 + 2.5t + 4.9t2 = 0 Solving -9 + 2.5t + 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'. -1.836734694 + 0.5102040816t + t2 = 0 Move the constant term to the right: Add '1.836734694' to each side of the equation. -1.836734694 + 0.5102040816t + 1.836734694 + t2 = 0 + 1.836734694 Reorder the terms: -1.836734694 + 1.836734694 + 0.5102040816t + t2 = 0 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + 0.5102040816t + t2 = 0 + 1.836734694 0.5102040816t + t2 = 0 + 1.836734694 Combine like terms: 0 + 1.836734694 = 1.836734694 0.5102040816t + t2 = 1.836734694 The t term is 0.5102040816t. Take half its coefficient (0.2551020408). Square it (0.06507705122) and add it to both sides. Add '0.06507705122' to each side of the equation. 0.5102040816t + 0.06507705122 + t2 = 1.836734694 + 0.06507705122 Reorder the terms: 0.06507705122 + 0.5102040816t + t2 = 1.836734694 + 0.06507705122 Combine like terms: 1.836734694 + 0.06507705122 = 1.90181174522 0.06507705122 + 0.5102040816t + t2 = 1.90181174522 Factor a perfect square on the left side: (t + 0.2551020408)(t + 0.2551020408) = 1.90181174522 Calculate the square root of the right side: 1.379061908 Break this problem into two subproblems by setting (t + 0.2551020408) equal to 1.379061908 and -1.379061908.Subproblem 1
t + 0.2551020408 = 1.379061908 Simplifying t + 0.2551020408 = 1.379061908 Reorder the terms: 0.2551020408 + t = 1.379061908 Solving 0.2551020408 + t = 1.379061908 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2551020408' to each side of the equation. 0.2551020408 + -0.2551020408 + t = 1.379061908 + -0.2551020408 Combine like terms: 0.2551020408 + -0.2551020408 = 0.0000000000 0.0000000000 + t = 1.379061908 + -0.2551020408 t = 1.379061908 + -0.2551020408 Combine like terms: 1.379061908 + -0.2551020408 = 1.1239598672 t = 1.1239598672 Simplifying t = 1.1239598672Subproblem 2
t + 0.2551020408 = -1.379061908 Simplifying t + 0.2551020408 = -1.379061908 Reorder the terms: 0.2551020408 + t = -1.379061908 Solving 0.2551020408 + t = -1.379061908 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2551020408' to each side of the equation. 0.2551020408 + -0.2551020408 + t = -1.379061908 + -0.2551020408 Combine like terms: 0.2551020408 + -0.2551020408 = 0.0000000000 0.0000000000 + t = -1.379061908 + -0.2551020408 t = -1.379061908 + -0.2551020408 Combine like terms: -1.379061908 + -0.2551020408 = -1.6341639488 t = -1.6341639488 Simplifying t = -1.6341639488Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.1239598672, -1.6341639488}
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