t^2+11t-30=0

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Solution for t^2+11t-30=0 equation:


Simplifying
t2 + 11t + -30 = 0

Reorder the terms:
-30 + 11t + t2 = 0

Solving
-30 + 11t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 11t + 30 + t2 = 0 + 30

Reorder the terms:
-30 + 30 + 11t + t2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 11t + t2 = 0 + 30
11t + t2 = 0 + 30

Combine like terms: 0 + 30 = 30
11t + t2 = 30

The t term is 11t.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11t + 30.25 + t2 = 30 + 30.25

Reorder the terms:
30.25 + 11t + t2 = 30 + 30.25

Combine like terms: 30 + 30.25 = 60.25
30.25 + 11t + t2 = 60.25

Factor a perfect square on the left side:
(t + 5.5)(t + 5.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(t + 5.5) equal to 7.762087348 and -7.762087348.

Subproblem 1

t + 5.5 = 7.762087348 Simplifying t + 5.5 = 7.762087348 Reorder the terms: 5.5 + t = 7.762087348 Solving 5.5 + t = 7.762087348 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + t = 7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + t = 7.762087348 + -5.5 t = 7.762087348 + -5.5 Combine like terms: 7.762087348 + -5.5 = 2.262087348 t = 2.262087348 Simplifying t = 2.262087348

Subproblem 2

t + 5.5 = -7.762087348 Simplifying t + 5.5 = -7.762087348 Reorder the terms: 5.5 + t = -7.762087348 Solving 5.5 + t = -7.762087348 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + t = -7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + t = -7.762087348 + -5.5 t = -7.762087348 + -5.5 Combine like terms: -7.762087348 + -5.5 = -13.262087348 t = -13.262087348 Simplifying t = -13.262087348

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.262087348, -13.262087348}

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