5t^2+23t+10=

Solution for 5t^2+23t+10= equation:

Simplifying
5t2 + 23t + 10 = 0

Reorder the terms:
10 + 23t + 5t2 = 0

Solving
10 + 23t + 5t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
2 + 4.6t + t2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 4.6t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + 4.6t + t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 4.6t + t2 = 0 + -2
4.6t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
4.6t + t2 = -2

The t term is 4.6t.  Take half its coefficient (2.3).
Square it (5.29) and add it to both sides.

Add '5.29' to each side of the equation.
4.6t + 5.29 + t2 = -2 + 5.29

Reorder the terms:
5.29 + 4.6t + t2 = -2 + 5.29

Combine like terms: -2 + 5.29 = 3.29
5.29 + 4.6t + t2 = 3.29

Factor a perfect square on the left side:
(t + 2.3)(t + 2.3) = 3.29

Calculate the square root of the right side: 1.813835715

Break this problem into two subproblems by setting 
(t + 2.3) equal to 1.813835715 and -1.813835715.

Subproblem 1
t + 2.3 = 1.813835715

Simplifying
t + 2.3 = 1.813835715

Reorder the terms:
2.3 + t = 1.813835715

Solving
2.3 + t = 1.813835715

Solving for variable 't'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + t = 1.813835715 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + t = 1.813835715 + -2.3
t = 1.813835715 + -2.3

Combine like terms: 1.813835715 + -2.3 = -0.486164285
t = -0.486164285

Simplifying
t = -0.486164285

Subproblem 2
t + 2.3 = -1.813835715

Simplifying
t + 2.3 = -1.813835715

Reorder the terms:
2.3 + t = -1.813835715

Solving
2.3 + t = -1.813835715

Solving for variable 't'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + t = -1.813835715 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + t = -1.813835715 + -2.3
t = -1.813835715 + -2.3

Combine like terms: -1.813835715 + -2.3 = -4.113835715
t = -4.113835715

Simplifying
t = -4.113835715

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.486164285, -4.113835715}