4t^2-15t-30=0

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Solution for 4t^2-15t-30=0 equation:


Simplifying
4t2 + -15t + -30 = 0

Reorder the terms:
-30 + -15t + 4t2 = 0

Solving
-30 + -15t + 4t2 = 0

Solving for variable 't'.

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

Divide each side by '4'.
-7.5 + -3.75t + t2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -3.75t + 7.5 + t2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -3.75t + t2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -3.75t + t2 = 0 + 7.5
-3.75t + t2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-3.75t + t2 = 7.5

The t term is -3.75t.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75t + 3.515625 + t2 = 7.5 + 3.515625

Reorder the terms:
3.515625 + -3.75t + t2 = 7.5 + 3.515625

Combine like terms: 7.5 + 3.515625 = 11.015625
3.515625 + -3.75t + t2 = 11.015625

Factor a perfect square on the left side:
(t + -1.875)(t + -1.875) = 11.015625

Calculate the square root of the right side: 3.318979512

Break this problem into two subproblems by setting 
(t + -1.875) equal to 3.318979512 and -3.318979512.

Subproblem 1

t + -1.875 = 3.318979512 Simplifying t + -1.875 = 3.318979512 Reorder the terms: -1.875 + t = 3.318979512 Solving -1.875 + t = 3.318979512 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = 3.318979512 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 3.318979512 + 1.875 t = 3.318979512 + 1.875 Combine like terms: 3.318979512 + 1.875 = 5.193979512 t = 5.193979512 Simplifying t = 5.193979512

Subproblem 2

t + -1.875 = -3.318979512 Simplifying t + -1.875 = -3.318979512 Reorder the terms: -1.875 + t = -3.318979512 Solving -1.875 + t = -3.318979512 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = -3.318979512 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -3.318979512 + 1.875 t = -3.318979512 + 1.875 Combine like terms: -3.318979512 + 1.875 = -1.443979512 t = -1.443979512 Simplifying t = -1.443979512

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.193979512, -1.443979512}

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