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Simplifying t2 + 14t + -49 = 0 Reorder the terms: -49 + 14t + t2 = 0 Solving -49 + 14t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 14t + 49 + t2 = 0 + 49 Reorder the terms: -49 + 49 + 14t + t2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 14t + t2 = 0 + 49 14t + t2 = 0 + 49 Combine like terms: 0 + 49 = 49 14t + t2 = 49 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 = 49 + 49 Reorder the terms: 49 + 14t + t2 = 49 + 49 Combine like terms: 49 + 49 = 98 49 + 14t + t2 = 98 Factor a perfect square on the left side: (t + 7)(t + 7) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (t + 7) equal to 9.899494937 and -9.899494937.Subproblem 1
t + 7 = 9.899494937 Simplifying t + 7 = 9.899494937 Reorder the terms: 7 + t = 9.899494937 Solving 7 + t = 9.899494937 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 = 9.899494937 + -7 Combine like terms: 7 + -7 = 0 0 + t = 9.899494937 + -7 t = 9.899494937 + -7 Combine like terms: 9.899494937 + -7 = 2.899494937 t = 2.899494937 Simplifying t = 2.899494937Subproblem 2
t + 7 = -9.899494937 Simplifying t + 7 = -9.899494937 Reorder the terms: 7 + t = -9.899494937 Solving 7 + t = -9.899494937 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 = -9.899494937 + -7 Combine like terms: 7 + -7 = 0 0 + t = -9.899494937 + -7 t = -9.899494937 + -7 Combine like terms: -9.899494937 + -7 = -16.899494937 t = -16.899494937 Simplifying t = -16.899494937Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.899494937, -16.899494937}
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