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Simplifying 5t2 + 2t = 3.9 Reorder the terms: 2t + 5t2 = 3.9 Solving 2t + 5t2 = 3.9 Solving for variable 't'. Reorder the terms: -3.9 + 2t + 5t2 = 3.9 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 -3.9 + 2t + 5t2 = 0.0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.78 + 0.4t + t2 = 0.0 Move the constant term to the right: Add '0.78' to each side of the equation. -0.78 + 0.4t + 0.78 + t2 = 0.0 + 0.78 Reorder the terms: -0.78 + 0.78 + 0.4t + t2 = 0.0 + 0.78 Combine like terms: -0.78 + 0.78 = 0.00 0.00 + 0.4t + t2 = 0.0 + 0.78 0.4t + t2 = 0.0 + 0.78 Combine like terms: 0.0 + 0.78 = 0.78 0.4t + t2 = 0.78 The t term is 0.4t. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4t + 0.04 + t2 = 0.78 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = 0.78 + 0.04 Combine like terms: 0.78 + 0.04 = 0.82 0.04 + 0.4t + t2 = 0.82 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 0.82 Calculate the square root of the right side: 0.905538514 Break this problem into two subproblems by setting (t + 0.2) equal to 0.905538514 and -0.905538514.Subproblem 1
t + 0.2 = 0.905538514 Simplifying t + 0.2 = 0.905538514 Reorder the terms: 0.2 + t = 0.905538514 Solving 0.2 + t = 0.905538514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = 0.905538514 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 0.905538514 + -0.2 t = 0.905538514 + -0.2 Combine like terms: 0.905538514 + -0.2 = 0.705538514 t = 0.705538514 Simplifying t = 0.705538514Subproblem 2
t + 0.2 = -0.905538514 Simplifying t + 0.2 = -0.905538514 Reorder the terms: 0.2 + t = -0.905538514 Solving 0.2 + t = -0.905538514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = -0.905538514 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -0.905538514 + -0.2 t = -0.905538514 + -0.2 Combine like terms: -0.905538514 + -0.2 = -1.105538514 t = -1.105538514 Simplifying t = -1.105538514Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.705538514, -1.105538514}
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