t^2+6=8t

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Solution for t^2+6=8t equation:


Simplifying
t2 + 6 = 8t

Reorder the terms:
6 + t2 = 8t

Solving
6 + t2 = 8t

Solving for variable 't'.

Reorder the terms:
6 + -8t + t2 = 8t + -8t

Combine like terms: 8t + -8t = 0
6 + -8t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -8t + -6 + t2 = 0 + -6

Reorder the terms:
6 + -6 + -8t + t2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -8t + t2 = 0 + -6
-8t + t2 = 0 + -6

Combine like terms: 0 + -6 = -6
-8t + t2 = -6

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 = -6 + 16

Reorder the terms:
16 + -8t + t2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + -8t + t2 = 10

Factor a perfect square on the left side:
(t + -4)(t + -4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(t + -4) equal to 3.16227766 and -3.16227766.

Subproblem 1

t + -4 = 3.16227766 Simplifying t + -4 = 3.16227766 Reorder the terms: -4 + t = 3.16227766 Solving -4 + t = 3.16227766 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 = 3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.16227766 + 4 t = 3.16227766 + 4 Combine like terms: 3.16227766 + 4 = 7.16227766 t = 7.16227766 Simplifying t = 7.16227766

Subproblem 2

t + -4 = -3.16227766 Simplifying t + -4 = -3.16227766 Reorder the terms: -4 + t = -3.16227766 Solving -4 + t = -3.16227766 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 = -3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.16227766 + 4 t = -3.16227766 + 4 Combine like terms: -3.16227766 + 4 = 0.83772234 t = 0.83772234 Simplifying t = 0.83772234

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.16227766, 0.83772234}

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