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Simplifying t2 + -14t + 34 = 0 Reorder the terms: 34 + -14t + t2 = 0 Solving 34 + -14t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -14t + -34 + t2 = 0 + -34 Reorder the terms: 34 + -34 + -14t + t2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -14t + t2 = 0 + -34 -14t + t2 = 0 + -34 Combine like terms: 0 + -34 = -34 -14t + t2 = -34 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 = -34 + 49 Reorder the terms: 49 + -14t + t2 = -34 + 49 Combine like terms: -34 + 49 = 15 49 + -14t + t2 = 15 Factor a perfect square on the left side: (t + -7)(t + -7) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (t + -7) equal to 3.872983346 and -3.872983346.Subproblem 1
t + -7 = 3.872983346 Simplifying t + -7 = 3.872983346 Reorder the terms: -7 + t = 3.872983346 Solving -7 + t = 3.872983346 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 = 3.872983346 + 7 Combine like terms: -7 + 7 = 0 0 + t = 3.872983346 + 7 t = 3.872983346 + 7 Combine like terms: 3.872983346 + 7 = 10.872983346 t = 10.872983346 Simplifying t = 10.872983346Subproblem 2
t + -7 = -3.872983346 Simplifying t + -7 = -3.872983346 Reorder the terms: -7 + t = -3.872983346 Solving -7 + t = -3.872983346 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 = -3.872983346 + 7 Combine like terms: -7 + 7 = 0 0 + t = -3.872983346 + 7 t = -3.872983346 + 7 Combine like terms: -3.872983346 + 7 = 3.127016654 t = 3.127016654 Simplifying t = 3.127016654Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.872983346, 3.127016654}
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