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Simplifying t2 + -28t + 124 = 0 Reorder the terms: 124 + -28t + t2 = 0 Solving 124 + -28t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-124' to each side of the equation. 124 + -28t + -124 + t2 = 0 + -124 Reorder the terms: 124 + -124 + -28t + t2 = 0 + -124 Combine like terms: 124 + -124 = 0 0 + -28t + t2 = 0 + -124 -28t + t2 = 0 + -124 Combine like terms: 0 + -124 = -124 -28t + t2 = -124 The t term is -28t. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28t + 196 + t2 = -124 + 196 Reorder the terms: 196 + -28t + t2 = -124 + 196 Combine like terms: -124 + 196 = 72 196 + -28t + t2 = 72 Factor a perfect square on the left side: (t + -14)(t + -14) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (t + -14) equal to 8.485281374 and -8.485281374.Subproblem 1
t + -14 = 8.485281374 Simplifying t + -14 = 8.485281374 Reorder the terms: -14 + t = 8.485281374 Solving -14 + t = 8.485281374 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + t = 8.485281374 + 14 Combine like terms: -14 + 14 = 0 0 + t = 8.485281374 + 14 t = 8.485281374 + 14 Combine like terms: 8.485281374 + 14 = 22.485281374 t = 22.485281374 Simplifying t = 22.485281374Subproblem 2
t + -14 = -8.485281374 Simplifying t + -14 = -8.485281374 Reorder the terms: -14 + t = -8.485281374 Solving -14 + t = -8.485281374 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + t = -8.485281374 + 14 Combine like terms: -14 + 14 = 0 0 + t = -8.485281374 + 14 t = -8.485281374 + 14 Combine like terms: -8.485281374 + 14 = 5.514718626 t = 5.514718626 Simplifying t = 5.514718626Solution
The solution to the problem is based on the solutions from the subproblems. t = {22.485281374, 5.514718626}
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