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Simplifying 151 = 235t + -1t2 Solving 151 = 235t + -1t2 Solving for variable 't'. Reorder the terms: 151 + -235t + t2 = 235t + -235t + -1t2 + t2 Combine like terms: 235t + -235t = 0 151 + -235t + t2 = 0 + -1t2 + t2 151 + -235t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 151 + -235t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-151' to each side of the equation. 151 + -235t + -151 + t2 = 0 + -151 Reorder the terms: 151 + -151 + -235t + t2 = 0 + -151 Combine like terms: 151 + -151 = 0 0 + -235t + t2 = 0 + -151 -235t + t2 = 0 + -151 Combine like terms: 0 + -151 = -151 -235t + t2 = -151 The t term is -235t. Take half its coefficient (-117.5). Square it (13806.25) and add it to both sides. Add '13806.25' to each side of the equation. -235t + 13806.25 + t2 = -151 + 13806.25 Reorder the terms: 13806.25 + -235t + t2 = -151 + 13806.25 Combine like terms: -151 + 13806.25 = 13655.25 13806.25 + -235t + t2 = 13655.25 Factor a perfect square on the left side: (t + -117.5)(t + -117.5) = 13655.25 Calculate the square root of the right side: 116.855680221 Break this problem into two subproblems by setting (t + -117.5) equal to 116.855680221 and -116.855680221.Subproblem 1
t + -117.5 = 116.855680221 Simplifying t + -117.5 = 116.855680221 Reorder the terms: -117.5 + t = 116.855680221 Solving -117.5 + t = 116.855680221 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '117.5' to each side of the equation. -117.5 + 117.5 + t = 116.855680221 + 117.5 Combine like terms: -117.5 + 117.5 = 0.0 0.0 + t = 116.855680221 + 117.5 t = 116.855680221 + 117.5 Combine like terms: 116.855680221 + 117.5 = 234.355680221 t = 234.355680221 Simplifying t = 234.355680221Subproblem 2
t + -117.5 = -116.855680221 Simplifying t + -117.5 = -116.855680221 Reorder the terms: -117.5 + t = -116.855680221 Solving -117.5 + t = -116.855680221 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '117.5' to each side of the equation. -117.5 + 117.5 + t = -116.855680221 + 117.5 Combine like terms: -117.5 + 117.5 = 0.0 0.0 + t = -116.855680221 + 117.5 t = -116.855680221 + 117.5 Combine like terms: -116.855680221 + 117.5 = 0.644319779 t = 0.644319779 Simplifying t = 0.644319779Solution
The solution to the problem is based on the solutions from the subproblems. t = {234.355680221, 0.644319779}
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