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Simplifying t2 + -14t + -22 = 0 Reorder the terms: -22 + -14t + t2 = 0 Solving -22 + -14t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -14t + 22 + t2 = 0 + 22 Reorder the terms: -22 + 22 + -14t + t2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -14t + t2 = 0 + 22 -14t + t2 = 0 + 22 Combine like terms: 0 + 22 = 22 -14t + t2 = 22 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 = 22 + 49 Reorder the terms: 49 + -14t + t2 = 22 + 49 Combine like terms: 22 + 49 = 71 49 + -14t + t2 = 71 Factor a perfect square on the left side: (t + -7)(t + -7) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (t + -7) equal to 8.426149773 and -8.426149773.Subproblem 1
t + -7 = 8.426149773 Simplifying t + -7 = 8.426149773 Reorder the terms: -7 + t = 8.426149773 Solving -7 + t = 8.426149773 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 = 8.426149773 + 7 Combine like terms: -7 + 7 = 0 0 + t = 8.426149773 + 7 t = 8.426149773 + 7 Combine like terms: 8.426149773 + 7 = 15.426149773 t = 15.426149773 Simplifying t = 15.426149773Subproblem 2
t + -7 = -8.426149773 Simplifying t + -7 = -8.426149773 Reorder the terms: -7 + t = -8.426149773 Solving -7 + t = -8.426149773 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 = -8.426149773 + 7 Combine like terms: -7 + 7 = 0 0 + t = -8.426149773 + 7 t = -8.426149773 + 7 Combine like terms: -8.426149773 + 7 = -1.426149773 t = -1.426149773 Simplifying t = -1.426149773Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.426149773, -1.426149773}
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