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Simplifying t2 + -112t + 160 = 0 Reorder the terms: 160 + -112t + t2 = 0 Solving 160 + -112t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-160' to each side of the equation. 160 + -112t + -160 + t2 = 0 + -160 Reorder the terms: 160 + -160 + -112t + t2 = 0 + -160 Combine like terms: 160 + -160 = 0 0 + -112t + t2 = 0 + -160 -112t + t2 = 0 + -160 Combine like terms: 0 + -160 = -160 -112t + t2 = -160 The t term is -112t. Take half its coefficient (-56). Square it (3136) and add it to both sides. Add '3136' to each side of the equation. -112t + 3136 + t2 = -160 + 3136 Reorder the terms: 3136 + -112t + t2 = -160 + 3136 Combine like terms: -160 + 3136 = 2976 3136 + -112t + t2 = 2976 Factor a perfect square on the left side: (t + -56)(t + -56) = 2976 Calculate the square root of the right side: 54.552726788 Break this problem into two subproblems by setting (t + -56) equal to 54.552726788 and -54.552726788.Subproblem 1
t + -56 = 54.552726788 Simplifying t + -56 = 54.552726788 Reorder the terms: -56 + t = 54.552726788 Solving -56 + t = 54.552726788 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + t = 54.552726788 + 56 Combine like terms: -56 + 56 = 0 0 + t = 54.552726788 + 56 t = 54.552726788 + 56 Combine like terms: 54.552726788 + 56 = 110.552726788 t = 110.552726788 Simplifying t = 110.552726788Subproblem 2
t + -56 = -54.552726788 Simplifying t + -56 = -54.552726788 Reorder the terms: -56 + t = -54.552726788 Solving -56 + t = -54.552726788 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + t = -54.552726788 + 56 Combine like terms: -56 + 56 = 0 0 + t = -54.552726788 + 56 t = -54.552726788 + 56 Combine like terms: -54.552726788 + 56 = 1.447273212 t = 1.447273212 Simplifying t = 1.447273212Solution
The solution to the problem is based on the solutions from the subproblems. t = {110.552726788, 1.447273212}
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