T^2+8T-7=0

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Solution for T^2+8T-7=0 equation: 


Simplifying
T2 + 8T + -7 = 0

Reorder the terms:
-7 + 8T + T2 = 0

Solving
-7 + 8T + T2 = 0

Solving for variable 'T'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 8T + 7 + T2 = 0 + 7

Reorder the terms:
-7 + 7 + 8T + T2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 8T + T2 = 0 + 7
8T + T2 = 0 + 7

Combine like terms: 0 + 7 = 7
8T + T2 = 7

The T term is 8T.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8T + 16 + T2 = 7 + 16

Reorder the terms:
16 + 8T + T2 = 7 + 16

Combine like terms: 7 + 16 = 23
16 + 8T + T2 = 23

Factor a perfect square on the left side:
(T + 4)(T + 4) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(T + 4) equal to 4.795831523 and -4.795831523.


Subproblem 1
T + 4 = 4.795831523

Simplifying
T + 4 = 4.795831523

Reorder the terms:
4 + T = 4.795831523

Solving
4 + T = 4.795831523

Solving for variable 'T'.

Move all terms containing T to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + T = 4.795831523 + -4

Combine like terms: 4 + -4 = 0
0 + T = 4.795831523 + -4
T = 4.795831523 + -4

Combine like terms: 4.795831523 + -4 = 0.795831523
T = 0.795831523

Simplifying
T = 0.795831523


Subproblem 2
T + 4 = -4.795831523

Simplifying
T + 4 = -4.795831523

Reorder the terms:
4 + T = -4.795831523

Solving
4 + T = -4.795831523

Solving for variable 'T'.

Move all terms containing T to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + T = -4.795831523 + -4

Combine like terms: 4 + -4 = 0
0 + T = -4.795831523 + -4
T = -4.795831523 + -4

Combine like terms: -4.795831523 + -4 = -8.795831523
T = -8.795831523

Simplifying
T = -8.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
T = {0.795831523, -8.795831523}

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