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Simplifying 4.9t2 + 2.5t + -58.0 = 0 Reorder the terms: -58.0 + 2.5t + 4.9t2 = 0 Solving -58.0 + 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'. -11.83673469 + 0.5102040816t + t2 = 0 Move the constant term to the right: Add '11.83673469' to each side of the equation. -11.83673469 + 0.5102040816t + 11.83673469 + t2 = 0 + 11.83673469 Reorder the terms: -11.83673469 + 11.83673469 + 0.5102040816t + t2 = 0 + 11.83673469 Combine like terms: -11.83673469 + 11.83673469 = 0.00000000 0.00000000 + 0.5102040816t + t2 = 0 + 11.83673469 0.5102040816t + t2 = 0 + 11.83673469 Combine like terms: 0 + 11.83673469 = 11.83673469 0.5102040816t + t2 = 11.83673469 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 = 11.83673469 + 0.06507705122 Reorder the terms: 0.06507705122 + 0.5102040816t + t2 = 11.83673469 + 0.06507705122 Combine like terms: 11.83673469 + 0.06507705122 = 11.90181174122 0.06507705122 + 0.5102040816t + t2 = 11.90181174122 Factor a perfect square on the left side: (t + 0.2551020408)(t + 0.2551020408) = 11.90181174122 Calculate the square root of the right side: 3.449900251 Break this problem into two subproblems by setting (t + 0.2551020408) equal to 3.449900251 and -3.449900251.Subproblem 1
t + 0.2551020408 = 3.449900251 Simplifying t + 0.2551020408 = 3.449900251 Reorder the terms: 0.2551020408 + t = 3.449900251 Solving 0.2551020408 + t = 3.449900251 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 = 3.449900251 + -0.2551020408 Combine like terms: 0.2551020408 + -0.2551020408 = 0.0000000000 0.0000000000 + t = 3.449900251 + -0.2551020408 t = 3.449900251 + -0.2551020408 Combine like terms: 3.449900251 + -0.2551020408 = 3.1947982102 t = 3.1947982102 Simplifying t = 3.1947982102Subproblem 2
t + 0.2551020408 = -3.449900251 Simplifying t + 0.2551020408 = -3.449900251 Reorder the terms: 0.2551020408 + t = -3.449900251 Solving 0.2551020408 + t = -3.449900251 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 = -3.449900251 + -0.2551020408 Combine like terms: 0.2551020408 + -0.2551020408 = 0.0000000000 0.0000000000 + t = -3.449900251 + -0.2551020408 t = -3.449900251 + -0.2551020408 Combine like terms: -3.449900251 + -0.2551020408 = -3.7050022918 t = -3.7050022918 Simplifying t = -3.7050022918Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.1947982102, -3.7050022918}
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