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Simplifying t2 + -36t + 256 = 0 Reorder the terms: 256 + -36t + t2 = 0 Solving 256 + -36t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-256' to each side of the equation. 256 + -36t + -256 + t2 = 0 + -256 Reorder the terms: 256 + -256 + -36t + t2 = 0 + -256 Combine like terms: 256 + -256 = 0 0 + -36t + t2 = 0 + -256 -36t + t2 = 0 + -256 Combine like terms: 0 + -256 = -256 -36t + t2 = -256 The t term is -36t. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36t + 324 + t2 = -256 + 324 Reorder the terms: 324 + -36t + t2 = -256 + 324 Combine like terms: -256 + 324 = 68 324 + -36t + t2 = 68 Factor a perfect square on the left side: (t + -18)(t + -18) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (t + -18) equal to 8.246211251 and -8.246211251.Subproblem 1
t + -18 = 8.246211251 Simplifying t + -18 = 8.246211251 Reorder the terms: -18 + t = 8.246211251 Solving -18 + t = 8.246211251 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + t = 8.246211251 + 18 Combine like terms: -18 + 18 = 0 0 + t = 8.246211251 + 18 t = 8.246211251 + 18 Combine like terms: 8.246211251 + 18 = 26.246211251 t = 26.246211251 Simplifying t = 26.246211251Subproblem 2
t + -18 = -8.246211251 Simplifying t + -18 = -8.246211251 Reorder the terms: -18 + t = -8.246211251 Solving -18 + t = -8.246211251 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + t = -8.246211251 + 18 Combine like terms: -18 + 18 = 0 0 + t = -8.246211251 + 18 t = -8.246211251 + 18 Combine like terms: -8.246211251 + 18 = 9.753788749 t = 9.753788749 Simplifying t = 9.753788749Solution
The solution to the problem is based on the solutions from the subproblems. t = {26.246211251, 9.753788749}
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