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Simplifying t2 + 7t = 11 Reorder the terms: 7t + t2 = 11 Solving 7t + t2 = 11 Solving for variable 't'. Reorder the terms: -11 + 7t + t2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 7t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 7t + 11 + t2 = 0 + 11 Reorder the terms: -11 + 11 + 7t + t2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 7t + t2 = 0 + 11 7t + t2 = 0 + 11 Combine like terms: 0 + 11 = 11 7t + t2 = 11 The t term is 7t. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7t + 12.25 + t2 = 11 + 12.25 Reorder the terms: 12.25 + 7t + t2 = 11 + 12.25 Combine like terms: 11 + 12.25 = 23.25 12.25 + 7t + t2 = 23.25 Factor a perfect square on the left side: (t + 3.5)(t + 3.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (t + 3.5) equal to 4.82182538 and -4.82182538.Subproblem 1
t + 3.5 = 4.82182538 Simplifying t + 3.5 = 4.82182538 Reorder the terms: 3.5 + t = 4.82182538 Solving 3.5 + t = 4.82182538 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + t = 4.82182538 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = 4.82182538 + -3.5 t = 4.82182538 + -3.5 Combine like terms: 4.82182538 + -3.5 = 1.32182538 t = 1.32182538 Simplifying t = 1.32182538Subproblem 2
t + 3.5 = -4.82182538 Simplifying t + 3.5 = -4.82182538 Reorder the terms: 3.5 + t = -4.82182538 Solving 3.5 + t = -4.82182538 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + t = -4.82182538 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = -4.82182538 + -3.5 t = -4.82182538 + -3.5 Combine like terms: -4.82182538 + -3.5 = -8.32182538 t = -8.32182538 Simplifying t = -8.32182538Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.32182538, -8.32182538}
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