5t*t-7t-60=0

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Solution for 5t*t-7t-60=0 equation:


Simplifying
5t * t + -7t + -60 = 0

Multiply t * t
5t2 + -7t + -60 = 0

Reorder the terms:
-60 + -7t + 5t2 = 0

Solving
-60 + -7t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
-12 + -1.4t + t2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -1.4t + 12 + t2 = 0 + 12

Reorder the terms:
-12 + 12 + -1.4t + t2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1.4t + t2 = 0 + 12
-1.4t + t2 = 0 + 12

Combine like terms: 0 + 12 = 12
-1.4t + t2 = 12

The t term is -1.4t.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4t + 0.49 + t2 = 12 + 0.49

Reorder the terms:
0.49 + -1.4t + t2 = 12 + 0.49

Combine like terms: 12 + 0.49 = 12.49
0.49 + -1.4t + t2 = 12.49

Factor a perfect square on the left side:
(t + -0.7)(t + -0.7) = 12.49

Calculate the square root of the right side: 3.534119409

Break this problem into two subproblems by setting 
(t + -0.7) equal to 3.534119409 and -3.534119409.

Subproblem 1

t + -0.7 = 3.534119409 Simplifying t + -0.7 = 3.534119409 Reorder the terms: -0.7 + t = 3.534119409 Solving -0.7 + t = 3.534119409 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = 3.534119409 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = 3.534119409 + 0.7 t = 3.534119409 + 0.7 Combine like terms: 3.534119409 + 0.7 = 4.234119409 t = 4.234119409 Simplifying t = 4.234119409

Subproblem 2

t + -0.7 = -3.534119409 Simplifying t + -0.7 = -3.534119409 Reorder the terms: -0.7 + t = -3.534119409 Solving -0.7 + t = -3.534119409 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = -3.534119409 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = -3.534119409 + 0.7 t = -3.534119409 + 0.7 Combine like terms: -3.534119409 + 0.7 = -2.834119409 t = -2.834119409 Simplifying t = -2.834119409

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.234119409, -2.834119409}

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