t^2+10t+12=0

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Solution for t^2+10t+12=0 equation:


Simplifying
t2 + 10t + 12 = 0

Reorder the terms:
12 + 10t + t2 = 0

Solving
12 + 10t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 10t + -12 + t2 = 0 + -12

Reorder the terms:
12 + -12 + 10t + t2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 10t + t2 = 0 + -12
10t + t2 = 0 + -12

Combine like terms: 0 + -12 = -12
10t + t2 = -12

The t term is 10t.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10t + 25 + t2 = -12 + 25

Reorder the terms:
25 + 10t + t2 = -12 + 25

Combine like terms: -12 + 25 = 13
25 + 10t + t2 = 13

Factor a perfect square on the left side:
(t + 5)(t + 5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(t + 5) equal to 3.605551275 and -3.605551275.

Subproblem 1

t + 5 = 3.605551275 Simplifying t + 5 = 3.605551275 Reorder the terms: 5 + t = 3.605551275 Solving 5 + t = 3.605551275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 3.605551275 + -5 Combine like terms: 5 + -5 = 0 0 + t = 3.605551275 + -5 t = 3.605551275 + -5 Combine like terms: 3.605551275 + -5 = -1.394448725 t = -1.394448725 Simplifying t = -1.394448725

Subproblem 2

t + 5 = -3.605551275 Simplifying t + 5 = -3.605551275 Reorder the terms: 5 + t = -3.605551275 Solving 5 + t = -3.605551275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -3.605551275 + -5 Combine like terms: 5 + -5 = 0 0 + t = -3.605551275 + -5 t = -3.605551275 + -5 Combine like terms: -3.605551275 + -5 = -8.605551275 t = -8.605551275 Simplifying t = -8.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-1.394448725, -8.605551275}

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