3t^2-24t=-30

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Solution for 3t^2-24t=-30 equation: 


Simplifying
3t2 + -24t = -30

Reorder the terms:
-24t + 3t2 = -30

Solving
-24t + 3t2 = -30

Solving for variable 't'.

Reorder the terms:
30 + -24t + 3t2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + -24t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -8t + t2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(10 + -8t + t2)' equal to zero and attempt to solve:

Simplifying
10 + -8t + t2 = 0

Solving
10 + -8t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -8t + -10 + t2 = 0 + -10

Reorder the terms:
10 + -10 + -8t + t2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -8t + t2 = 0 + -10
-8t + t2 = 0 + -10

Combine like terms: 0 + -10 = -10
-8t + t2 = -10

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 = -10 + 16

Reorder the terms:
16 + -8t + t2 = -10 + 16

Combine like terms: -10 + 16 = 6
16 + -8t + t2 = 6

Factor a perfect square on the left side:
(t + -4)(t + -4) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(t + -4) equal to 2.449489743 and -2.449489743.


Subproblem 1
t + -4 = 2.449489743

Simplifying
t + -4 = 2.449489743

Reorder the terms:
-4 + t = 2.449489743

Solving
-4 + t = 2.449489743

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 = 2.449489743 + 4

Combine like terms: -4 + 4 = 0
0 + t = 2.449489743 + 4
t = 2.449489743 + 4

Combine like terms: 2.449489743 + 4 = 6.449489743
t = 6.449489743

Simplifying
t = 6.449489743


Subproblem 2
t + -4 = -2.449489743

Simplifying
t + -4 = -2.449489743

Reorder the terms:
-4 + t = -2.449489743

Solving
-4 + t = -2.449489743

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 = -2.449489743 + 4

Combine like terms: -4 + 4 = 0
0 + t = -2.449489743 + 4
t = -2.449489743 + 4

Combine like terms: -2.449489743 + 4 = 1.550510257
t = 1.550510257

Simplifying
t = 1.550510257


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.449489743, 1.550510257}
Solution
t = {6.449489743, 1.550510257}

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