(4t^2)-35t-45=0

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Solution for (4t^2)-35t-45=0 equation:


Simplifying
(4t2) + -35t + -45 = 0

Reorder the terms:
-45 + -35t + (4t2) = 0

Solving
-45 + -35t + (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'.
-11.25 + -8.75t + t2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -8.75t + 11.25 + t2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -8.75t + t2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -8.75t + t2 = 0 + 11.25
-8.75t + t2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-8.75t + t2 = 11.25

The t term is -8.75t.  Take half its coefficient (-4.375).
Square it (19.140625) and add it to both sides.

Add '19.140625' to each side of the equation.
-8.75t + 19.140625 + t2 = 11.25 + 19.140625

Reorder the terms:
19.140625 + -8.75t + t2 = 11.25 + 19.140625

Combine like terms: 11.25 + 19.140625 = 30.390625
19.140625 + -8.75t + t2 = 30.390625

Factor a perfect square on the left side:
((t) + -4.375)((t) + -4.375) = 30.390625

Calculate the square root of the right side: 5.512769268

Break this problem into two subproblems by setting 
((t) + -4.375) equal to 5.512769268 and -5.512769268.

Subproblem 1

(t) + -4.375 = 5.512769268 Simplifying (t) + -4.375 = 5.512769268 t + -4.375 = 5.512769268 Reorder the terms: -4.375 + t = 5.512769268 Solving -4.375 + t = 5.512769268 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + t = 5.512769268 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = 5.512769268 + 4.375 t = 5.512769268 + 4.375 Combine like terms: 5.512769268 + 4.375 = 9.887769268 t = 9.887769268 Simplifying t = 9.887769268

Subproblem 2

(t) + -4.375 = -5.512769268 Simplifying (t) + -4.375 = -5.512769268 t + -4.375 = -5.512769268 Reorder the terms: -4.375 + t = -5.512769268 Solving -4.375 + t = -5.512769268 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + t = -5.512769268 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = -5.512769268 + 4.375 t = -5.512769268 + 4.375 Combine like terms: -5.512769268 + 4.375 = -1.137769268 t = -1.137769268 Simplifying t = -1.137769268

Solution

The solution to the problem is based on the solutions from the subproblems. t = {9.887769268, -1.137769268}

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