t^2+8t-72=0

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Solution for t^2+8t-72=0 equation:


Simplifying
t2 + 8t + -72 = 0

Reorder the terms:
-72 + 8t + t2 = 0

Solving
-72 + 8t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 8t + 72 + t2 = 0 + 72

Reorder the terms:
-72 + 72 + 8t + t2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 8t + t2 = 0 + 72
8t + t2 = 0 + 72

Combine like terms: 0 + 72 = 72
8t + t2 = 72

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 = 72 + 16

Reorder the terms:
16 + 8t + t2 = 72 + 16

Combine like terms: 72 + 16 = 88
16 + 8t + t2 = 88

Factor a perfect square on the left side:
(t + 4)(t + 4) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(t + 4) equal to 9.38083152 and -9.38083152.

Subproblem 1

t + 4 = 9.38083152 Simplifying t + 4 = 9.38083152 Reorder the terms: 4 + t = 9.38083152 Solving 4 + t = 9.38083152 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 = 9.38083152 + -4 Combine like terms: 4 + -4 = 0 0 + t = 9.38083152 + -4 t = 9.38083152 + -4 Combine like terms: 9.38083152 + -4 = 5.38083152 t = 5.38083152 Simplifying t = 5.38083152

Subproblem 2

t + 4 = -9.38083152 Simplifying t + 4 = -9.38083152 Reorder the terms: 4 + t = -9.38083152 Solving 4 + t = -9.38083152 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 = -9.38083152 + -4 Combine like terms: 4 + -4 = 0 0 + t = -9.38083152 + -4 t = -9.38083152 + -4 Combine like terms: -9.38083152 + -4 = -13.38083152 t = -13.38083152 Simplifying t = -13.38083152

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.38083152, -13.38083152}

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