t^2+10t-4=0

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Solution for t^2+10t-4=0 equation:


Simplifying
t2 + 10t + -4 = 0

Reorder the terms:
-4 + 10t + t2 = 0

Solving
-4 + 10t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 10t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + 10t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 10t + t2 = 0 + 4
10t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
10t + t2 = 4

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 = 4 + 25

Reorder the terms:
25 + 10t + t2 = 4 + 25

Combine like terms: 4 + 25 = 29
25 + 10t + t2 = 29

Factor a perfect square on the left side:
(t + 5)(t + 5) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(t + 5) equal to 5.385164807 and -5.385164807.

Subproblem 1

t + 5 = 5.385164807 Simplifying t + 5 = 5.385164807 Reorder the terms: 5 + t = 5.385164807 Solving 5 + t = 5.385164807 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 = 5.385164807 + -5 Combine like terms: 5 + -5 = 0 0 + t = 5.385164807 + -5 t = 5.385164807 + -5 Combine like terms: 5.385164807 + -5 = 0.385164807 t = 0.385164807 Simplifying t = 0.385164807

Subproblem 2

t + 5 = -5.385164807 Simplifying t + 5 = -5.385164807 Reorder the terms: 5 + t = -5.385164807 Solving 5 + t = -5.385164807 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 = -5.385164807 + -5 Combine like terms: 5 + -5 = 0 0 + t = -5.385164807 + -5 t = -5.385164807 + -5 Combine like terms: -5.385164807 + -5 = -10.385164807 t = -10.385164807 Simplifying t = -10.385164807

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.385164807, -10.385164807}

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