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Simplifying t2 + 16t + -9 = 0 Reorder the terms: -9 + 16t + t2 = 0 Solving -9 + 16t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 16t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + 16t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 16t + t2 = 0 + 9 16t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 16t + t2 = 9 The t term is 16t. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16t + 64 + t2 = 9 + 64 Reorder the terms: 64 + 16t + t2 = 9 + 64 Combine like terms: 9 + 64 = 73 64 + 16t + t2 = 73 Factor a perfect square on the left side: (t + 8)(t + 8) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (t + 8) equal to 8.544003745 and -8.544003745.Subproblem 1
t + 8 = 8.544003745 Simplifying t + 8 = 8.544003745 Reorder the terms: 8 + t = 8.544003745 Solving 8 + t = 8.544003745 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = 8.544003745 + -8 Combine like terms: 8 + -8 = 0 0 + t = 8.544003745 + -8 t = 8.544003745 + -8 Combine like terms: 8.544003745 + -8 = 0.544003745 t = 0.544003745 Simplifying t = 0.544003745Subproblem 2
t + 8 = -8.544003745 Simplifying t + 8 = -8.544003745 Reorder the terms: 8 + t = -8.544003745 Solving 8 + t = -8.544003745 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = -8.544003745 + -8 Combine like terms: 8 + -8 = 0 0 + t = -8.544003745 + -8 t = -8.544003745 + -8 Combine like terms: -8.544003745 + -8 = -16.544003745 t = -16.544003745 Simplifying t = -16.544003745Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.544003745, -16.544003745}
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