t^2-16t=25

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Solution for t^2-16t=25 equation:


Simplifying
t2 + -16t = 25

Reorder the terms:
-16t + t2 = 25

Solving
-16t + t2 = 25

Solving for variable 't'.

Reorder the terms:
-25 + -16t + t2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -16t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -16t + 25 + t2 = 0 + 25

Reorder the terms:
-25 + 25 + -16t + t2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -16t + t2 = 0 + 25
-16t + t2 = 0 + 25

Combine like terms: 0 + 25 = 25
-16t + t2 = 25

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 = 25 + 64

Reorder the terms:
64 + -16t + t2 = 25 + 64

Combine like terms: 25 + 64 = 89
64 + -16t + t2 = 89

Factor a perfect square on the left side:
(t + -8)(t + -8) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(t + -8) equal to 9.433981132 and -9.433981132.

Subproblem 1

t + -8 = 9.433981132 Simplifying t + -8 = 9.433981132 Reorder the terms: -8 + t = 9.433981132 Solving -8 + t = 9.433981132 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 = 9.433981132 + 8 Combine like terms: -8 + 8 = 0 0 + t = 9.433981132 + 8 t = 9.433981132 + 8 Combine like terms: 9.433981132 + 8 = 17.433981132 t = 17.433981132 Simplifying t = 17.433981132

Subproblem 2

t + -8 = -9.433981132 Simplifying t + -8 = -9.433981132 Reorder the terms: -8 + t = -9.433981132 Solving -8 + t = -9.433981132 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 = -9.433981132 + 8 Combine like terms: -8 + 8 = 0 0 + t = -9.433981132 + 8 t = -9.433981132 + 8 Combine like terms: -9.433981132 + 8 = -1.433981132 t = -1.433981132 Simplifying t = -1.433981132

Solution

The solution to the problem is based on the solutions from the subproblems. t = {17.433981132, -1.433981132}

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