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Simplifying 34 = 6t + t2 Solving 34 = 6t + t2 Solving for variable 't'. Reorder the terms: 34 + -6t + -1t2 = 6t + -6t + t2 + -1t2 Combine like terms: 6t + -6t = 0 34 + -6t + -1t2 = 0 + t2 + -1t2 34 + -6t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 34 + -6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -34 + 6t + t2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + 6t + 34 + t2 = 0 + 34 Reorder the terms: -34 + 34 + 6t + t2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 6t + t2 = 0 + 34 6t + t2 = 0 + 34 Combine like terms: 0 + 34 = 34 6t + t2 = 34 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 = 34 + 9 Reorder the terms: 9 + 6t + t2 = 34 + 9 Combine like terms: 34 + 9 = 43 9 + 6t + t2 = 43 Factor a perfect square on the left side: (t + 3)(t + 3) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (t + 3) equal to 6.557438524 and -6.557438524.Subproblem 1
t + 3 = 6.557438524 Simplifying t + 3 = 6.557438524 Reorder the terms: 3 + t = 6.557438524 Solving 3 + t = 6.557438524 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 = 6.557438524 + -3 Combine like terms: 3 + -3 = 0 0 + t = 6.557438524 + -3 t = 6.557438524 + -3 Combine like terms: 6.557438524 + -3 = 3.557438524 t = 3.557438524 Simplifying t = 3.557438524Subproblem 2
t + 3 = -6.557438524 Simplifying t + 3 = -6.557438524 Reorder the terms: 3 + t = -6.557438524 Solving 3 + t = -6.557438524 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 = -6.557438524 + -3 Combine like terms: 3 + -3 = 0 0 + t = -6.557438524 + -3 t = -6.557438524 + -3 Combine like terms: -6.557438524 + -3 = -9.557438524 t = -9.557438524 Simplifying t = -9.557438524Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.557438524, -9.557438524}
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