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Simplifying t2 + -14t + -41 = 0 Reorder the terms: -41 + -14t + t2 = 0 Solving -41 + -14t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -14t + 41 + t2 = 0 + 41 Reorder the terms: -41 + 41 + -14t + t2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -14t + t2 = 0 + 41 -14t + t2 = 0 + 41 Combine like terms: 0 + 41 = 41 -14t + t2 = 41 The t term is -14t. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14t + 49 + t2 = 41 + 49 Reorder the terms: 49 + -14t + t2 = 41 + 49 Combine like terms: 41 + 49 = 90 49 + -14t + t2 = 90 Factor a perfect square on the left side: (t + -7)(t + -7) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (t + -7) equal to 9.486832981 and -9.486832981.Subproblem 1
t + -7 = 9.486832981 Simplifying t + -7 = 9.486832981 Reorder the terms: -7 + t = 9.486832981 Solving -7 + t = 9.486832981 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = 9.486832981 + 7 Combine like terms: -7 + 7 = 0 0 + t = 9.486832981 + 7 t = 9.486832981 + 7 Combine like terms: 9.486832981 + 7 = 16.486832981 t = 16.486832981 Simplifying t = 16.486832981Subproblem 2
t + -7 = -9.486832981 Simplifying t + -7 = -9.486832981 Reorder the terms: -7 + t = -9.486832981 Solving -7 + t = -9.486832981 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = -9.486832981 + 7 Combine like terms: -7 + 7 = 0 0 + t = -9.486832981 + 7 t = -9.486832981 + 7 Combine like terms: -9.486832981 + 7 = -2.486832981 t = -2.486832981 Simplifying t = -2.486832981Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.486832981, -2.486832981}
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