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Simplifying t2 + -48t + 68 = 0 Reorder the terms: 68 + -48t + t2 = 0 Solving 68 + -48t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-68' to each side of the equation. 68 + -48t + -68 + t2 = 0 + -68 Reorder the terms: 68 + -68 + -48t + t2 = 0 + -68 Combine like terms: 68 + -68 = 0 0 + -48t + t2 = 0 + -68 -48t + t2 = 0 + -68 Combine like terms: 0 + -68 = -68 -48t + t2 = -68 The t term is -48t. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48t + 576 + t2 = -68 + 576 Reorder the terms: 576 + -48t + t2 = -68 + 576 Combine like terms: -68 + 576 = 508 576 + -48t + t2 = 508 Factor a perfect square on the left side: (t + -24)(t + -24) = 508 Calculate the square root of the right side: 22.538855339 Break this problem into two subproblems by setting (t + -24) equal to 22.538855339 and -22.538855339.Subproblem 1
t + -24 = 22.538855339 Simplifying t + -24 = 22.538855339 Reorder the terms: -24 + t = 22.538855339 Solving -24 + t = 22.538855339 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + t = 22.538855339 + 24 Combine like terms: -24 + 24 = 0 0 + t = 22.538855339 + 24 t = 22.538855339 + 24 Combine like terms: 22.538855339 + 24 = 46.538855339 t = 46.538855339 Simplifying t = 46.538855339Subproblem 2
t + -24 = -22.538855339 Simplifying t + -24 = -22.538855339 Reorder the terms: -24 + t = -22.538855339 Solving -24 + t = -22.538855339 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + t = -22.538855339 + 24 Combine like terms: -24 + 24 = 0 0 + t = -22.538855339 + 24 t = -22.538855339 + 24 Combine like terms: -22.538855339 + 24 = 1.461144661 t = 1.461144661 Simplifying t = 1.461144661Solution
The solution to the problem is based on the solutions from the subproblems. t = {46.538855339, 1.461144661}
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