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Simplifying t2 + 14t + 11 = 0 Reorder the terms: 11 + 14t + t2 = 0 Solving 11 + 14t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 14t + -11 + t2 = 0 + -11 Reorder the terms: 11 + -11 + 14t + t2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 14t + t2 = 0 + -11 14t + t2 = 0 + -11 Combine like terms: 0 + -11 = -11 14t + t2 = -11 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 = -11 + 49 Reorder the terms: 49 + 14t + t2 = -11 + 49 Combine like terms: -11 + 49 = 38 49 + 14t + t2 = 38 Factor a perfect square on the left side: (t + 7)(t + 7) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (t + 7) equal to 6.164414003 and -6.164414003.Subproblem 1
t + 7 = 6.164414003 Simplifying t + 7 = 6.164414003 Reorder the terms: 7 + t = 6.164414003 Solving 7 + t = 6.164414003 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 = 6.164414003 + -7 Combine like terms: 7 + -7 = 0 0 + t = 6.164414003 + -7 t = 6.164414003 + -7 Combine like terms: 6.164414003 + -7 = -0.835585997 t = -0.835585997 Simplifying t = -0.835585997Subproblem 2
t + 7 = -6.164414003 Simplifying t + 7 = -6.164414003 Reorder the terms: 7 + t = -6.164414003 Solving 7 + t = -6.164414003 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 = -6.164414003 + -7 Combine like terms: 7 + -7 = 0 0 + t = -6.164414003 + -7 t = -6.164414003 + -7 Combine like terms: -6.164414003 + -7 = -13.164414003 t = -13.164414003 Simplifying t = -13.164414003Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.835585997, -13.164414003}
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