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Simplifying t2 + 12t = 84 Reorder the terms: 12t + t2 = 84 Solving 12t + t2 = 84 Solving for variable 't'. Reorder the terms: -84 + 12t + t2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 12t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 12t + 84 + t2 = 0 + 84 Reorder the terms: -84 + 84 + 12t + t2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 12t + t2 = 0 + 84 12t + t2 = 0 + 84 Combine like terms: 0 + 84 = 84 12t + t2 = 84 The t term is 12t. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12t + 36 + t2 = 84 + 36 Reorder the terms: 36 + 12t + t2 = 84 + 36 Combine like terms: 84 + 36 = 120 36 + 12t + t2 = 120 Factor a perfect square on the left side: (t + 6)(t + 6) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (t + 6) equal to 10.95445115 and -10.95445115.Subproblem 1
t + 6 = 10.95445115 Simplifying t + 6 = 10.95445115 Reorder the terms: 6 + t = 10.95445115 Solving 6 + t = 10.95445115 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = 10.95445115 + -6 Combine like terms: 6 + -6 = 0 0 + t = 10.95445115 + -6 t = 10.95445115 + -6 Combine like terms: 10.95445115 + -6 = 4.95445115 t = 4.95445115 Simplifying t = 4.95445115Subproblem 2
t + 6 = -10.95445115 Simplifying t + 6 = -10.95445115 Reorder the terms: 6 + t = -10.95445115 Solving 6 + t = -10.95445115 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = -10.95445115 + -6 Combine like terms: 6 + -6 = 0 0 + t = -10.95445115 + -6 t = -10.95445115 + -6 Combine like terms: -10.95445115 + -6 = -16.95445115 t = -16.95445115 Simplifying t = -16.95445115Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.95445115, -16.95445115}
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