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Simplifying t(t + 11) = 70 Reorder the terms: t(11 + t) = 70 (11 * t + t * t) = 70 (11t + t2) = 70 Solving 11t + t2 = 70 Solving for variable 't'. Reorder the terms: -70 + 11t + t2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + 11t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + 11t + 70 + t2 = 0 + 70 Reorder the terms: -70 + 70 + 11t + t2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 11t + t2 = 0 + 70 11t + t2 = 0 + 70 Combine like terms: 0 + 70 = 70 11t + t2 = 70 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 = 70 + 30.25 Reorder the terms: 30.25 + 11t + t2 = 70 + 30.25 Combine like terms: 70 + 30.25 = 100.25 30.25 + 11t + t2 = 100.25 Factor a perfect square on the left side: (t + 5.5)(t + 5.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (t + 5.5) equal to 10.012492197 and -10.012492197.Subproblem 1
t + 5.5 = 10.012492197 Simplifying t + 5.5 = 10.012492197 Reorder the terms: 5.5 + t = 10.012492197 Solving 5.5 + t = 10.012492197 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 = 10.012492197 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + t = 10.012492197 + -5.5 t = 10.012492197 + -5.5 Combine like terms: 10.012492197 + -5.5 = 4.512492197 t = 4.512492197 Simplifying t = 4.512492197Subproblem 2
t + 5.5 = -10.012492197 Simplifying t + 5.5 = -10.012492197 Reorder the terms: 5.5 + t = -10.012492197 Solving 5.5 + t = -10.012492197 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 = -10.012492197 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + t = -10.012492197 + -5.5 t = -10.012492197 + -5.5 Combine like terms: -10.012492197 + -5.5 = -15.512492197 t = -15.512492197 Simplifying t = -15.512492197Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.512492197, -15.512492197}
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