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Simplifying t2 + -11t + 7 = 0 Reorder the terms: 7 + -11t + t2 = 0 Solving 7 + -11t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -11t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + -11t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -11t + t2 = 0 + -7 -11t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 -11t + t2 = -7 The t term is -11t. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11t + 30.25 + t2 = -7 + 30.25 Reorder the terms: 30.25 + -11t + t2 = -7 + 30.25 Combine like terms: -7 + 30.25 = 23.25 30.25 + -11t + t2 = 23.25 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (t + -5.5) equal to 4.82182538 and -4.82182538.Subproblem 1
t + -5.5 = 4.82182538 Simplifying t + -5.5 = 4.82182538 Reorder the terms: -5.5 + t = 4.82182538 Solving -5.5 + t = 4.82182538 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = 4.82182538 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 4.82182538 + 5.5 t = 4.82182538 + 5.5 Combine like terms: 4.82182538 + 5.5 = 10.32182538 t = 10.32182538 Simplifying t = 10.32182538Subproblem 2
t + -5.5 = -4.82182538 Simplifying t + -5.5 = -4.82182538 Reorder the terms: -5.5 + t = -4.82182538 Solving -5.5 + t = -4.82182538 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = -4.82182538 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -4.82182538 + 5.5 t = -4.82182538 + 5.5 Combine like terms: -4.82182538 + 5.5 = 0.67817462 t = 0.67817462 Simplifying t = 0.67817462Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.32182538, 0.67817462}
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