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Simplifying 35 = (t(t)) + 6t Multiply t * t 35 = (t2) + 6t 35 = t2 + 6t Reorder the terms: 35 = 6t + t2 Solving 35 = 6t + t2 Solving for variable 't'. Reorder the terms: 35 + -6t + -1t2 = 6t + -6t + t2 + -1t2 Combine like terms: 6t + -6t = 0 35 + -6t + -1t2 = 0 + t2 + -1t2 35 + -6t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 35 + -6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + 6t + t2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 6t + 35 + t2 = 0 + 35 Reorder the terms: -35 + 35 + 6t + t2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 6t + t2 = 0 + 35 6t + t2 = 0 + 35 Combine like terms: 0 + 35 = 35 6t + t2 = 35 The t term is 6t. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t + 9 + t2 = 35 + 9 Reorder the terms: 9 + 6t + t2 = 35 + 9 Combine like terms: 35 + 9 = 44 9 + 6t + t2 = 44 Factor a perfect square on the left side: (t + 3)(t + 3) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (t + 3) equal to 6.633249581 and -6.633249581.Subproblem 1
t + 3 = 6.633249581 Simplifying t + 3 = 6.633249581 Reorder the terms: 3 + t = 6.633249581 Solving 3 + t = 6.633249581 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 6.633249581 + -3 Combine like terms: 3 + -3 = 0 0 + t = 6.633249581 + -3 t = 6.633249581 + -3 Combine like terms: 6.633249581 + -3 = 3.633249581 t = 3.633249581 Simplifying t = 3.633249581Subproblem 2
t + 3 = -6.633249581 Simplifying t + 3 = -6.633249581 Reorder the terms: 3 + t = -6.633249581 Solving 3 + t = -6.633249581 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = -6.633249581 + -3 Combine like terms: 3 + -3 = 0 0 + t = -6.633249581 + -3 t = -6.633249581 + -3 Combine like terms: -6.633249581 + -3 = -9.633249581 t = -9.633249581 Simplifying t = -9.633249581Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.633249581, -9.633249581}
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