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Simplifying 2.5t + 4.9t2 + -120 = 0 Reorder the terms: -120 + 2.5t + 4.9t2 = 0 Solving -120 + 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'. -24.48979592 + 0.5102040816t + t2 = 0 Move the constant term to the right: Add '24.48979592' to each side of the equation. -24.48979592 + 0.5102040816t + 24.48979592 + t2 = 0 + 24.48979592 Reorder the terms: -24.48979592 + 24.48979592 + 0.5102040816t + t2 = 0 + 24.48979592 Combine like terms: -24.48979592 + 24.48979592 = 0.00000000 0.00000000 + 0.5102040816t + t2 = 0 + 24.48979592 0.5102040816t + t2 = 0 + 24.48979592 Combine like terms: 0 + 24.48979592 = 24.48979592 0.5102040816t + t2 = 24.48979592 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 = 24.48979592 + 0.06507705122 Reorder the terms: 0.06507705122 + 0.5102040816t + t2 = 24.48979592 + 0.06507705122 Combine like terms: 24.48979592 + 0.06507705122 = 24.55487297122 0.06507705122 + 0.5102040816t + t2 = 24.55487297122 Factor a perfect square on the left side: (t + 0.2551020408)(t + 0.2551020408) = 24.55487297122 Calculate the square root of the right side: 4.955287375 Break this problem into two subproblems by setting (t + 0.2551020408) equal to 4.955287375 and -4.955287375.Subproblem 1
t + 0.2551020408 = 4.955287375 Simplifying t + 0.2551020408 = 4.955287375 Reorder the terms: 0.2551020408 + t = 4.955287375 Solving 0.2551020408 + t = 4.955287375 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 = 4.955287375 + -0.2551020408 Combine like terms: 0.2551020408 + -0.2551020408 = 0.0000000000 0.0000000000 + t = 4.955287375 + -0.2551020408 t = 4.955287375 + -0.2551020408 Combine like terms: 4.955287375 + -0.2551020408 = 4.7001853342 t = 4.7001853342 Simplifying t = 4.7001853342Subproblem 2
t + 0.2551020408 = -4.955287375 Simplifying t + 0.2551020408 = -4.955287375 Reorder the terms: 0.2551020408 + t = -4.955287375 Solving 0.2551020408 + t = -4.955287375 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 = -4.955287375 + -0.2551020408 Combine like terms: 0.2551020408 + -0.2551020408 = 0.0000000000 0.0000000000 + t = -4.955287375 + -0.2551020408 t = -4.955287375 + -0.2551020408 Combine like terms: -4.955287375 + -0.2551020408 = -5.2103894158 t = -5.2103894158 Simplifying t = -5.2103894158Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.7001853342, -5.2103894158}
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