3t^2+2t-30=0

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Solution for 3t^2+2t-30=0 equation:


Simplifying
3t2 + 2t + -30 = 0

Reorder the terms:
-30 + 2t + 3t2 = 0

Solving
-30 + 2t + 3t2 = 0

Solving for variable 't'.

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

Divide each side by '3'.
-10 + 0.6666666667t + t2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 0.6666666667t + 10 + t2 = 0 + 10

Reorder the terms:
-10 + 10 + 0.6666666667t + t2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 0.6666666667t + t2 = 0 + 10
0.6666666667t + t2 = 0 + 10

Combine like terms: 0 + 10 = 10
0.6666666667t + t2 = 10

The t term is 0.6666666667t.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667t + 0.1111111112 + t2 = 10 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667t + t2 = 10 + 0.1111111112

Combine like terms: 10 + 0.1111111112 = 10.1111111112
0.1111111112 + 0.6666666667t + t2 = 10.1111111112

Factor a perfect square on the left side:
(t + 0.3333333334)(t + 0.3333333334) = 10.1111111112

Calculate the square root of the right side: 3.179797338

Break this problem into two subproblems by setting 
(t + 0.3333333334) equal to 3.179797338 and -3.179797338.

Subproblem 1

t + 0.3333333334 = 3.179797338 Simplifying t + 0.3333333334 = 3.179797338 Reorder the terms: 0.3333333334 + t = 3.179797338 Solving 0.3333333334 + t = 3.179797338 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + t = 3.179797338 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + t = 3.179797338 + -0.3333333334 t = 3.179797338 + -0.3333333334 Combine like terms: 3.179797338 + -0.3333333334 = 2.8464640046 t = 2.8464640046 Simplifying t = 2.8464640046

Subproblem 2

t + 0.3333333334 = -3.179797338 Simplifying t + 0.3333333334 = -3.179797338 Reorder the terms: 0.3333333334 + t = -3.179797338 Solving 0.3333333334 + t = -3.179797338 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + t = -3.179797338 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + t = -3.179797338 + -0.3333333334 t = -3.179797338 + -0.3333333334 Combine like terms: -3.179797338 + -0.3333333334 = -3.5131306714 t = -3.5131306714 Simplifying t = -3.5131306714

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.8464640046, -3.5131306714}

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