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Simplifying 5t2 + 6t = 35 Reorder the terms: 6t + 5t2 = 35 Solving 6t + 5t2 = 35 Solving for variable 't'. Reorder the terms: -35 + 6t + 5t2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 6t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7 + 1.2t + t2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 1.2t + 7 + t2 = 0 + 7 Reorder the terms: -7 + 7 + 1.2t + t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 1.2t + t2 = 0 + 7 1.2t + t2 = 0 + 7 Combine like terms: 0 + 7 = 7 1.2t + t2 = 7 The t term is 1.2t. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2t + 0.36 + t2 = 7 + 0.36 Reorder the terms: 0.36 + 1.2t + t2 = 7 + 0.36 Combine like terms: 7 + 0.36 = 7.36 0.36 + 1.2t + t2 = 7.36 Factor a perfect square on the left side: (t + 0.6)(t + 0.6) = 7.36 Calculate the square root of the right side: 2.712931993 Break this problem into two subproblems by setting (t + 0.6) equal to 2.712931993 and -2.712931993.Subproblem 1
t + 0.6 = 2.712931993 Simplifying t + 0.6 = 2.712931993 Reorder the terms: 0.6 + t = 2.712931993 Solving 0.6 + t = 2.712931993 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = 2.712931993 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = 2.712931993 + -0.6 t = 2.712931993 + -0.6 Combine like terms: 2.712931993 + -0.6 = 2.112931993 t = 2.112931993 Simplifying t = 2.112931993Subproblem 2
t + 0.6 = -2.712931993 Simplifying t + 0.6 = -2.712931993 Reorder the terms: 0.6 + t = -2.712931993 Solving 0.6 + t = -2.712931993 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = -2.712931993 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = -2.712931993 + -0.6 t = -2.712931993 + -0.6 Combine like terms: -2.712931993 + -0.6 = -3.312931993 t = -3.312931993 Simplifying t = -3.312931993Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.112931993, -3.312931993}
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