4t^2-11t-500=0

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Solution for 4t^2-11t-500=0 equation:


Simplifying
4t2 + -11t + -500 = 0

Reorder the terms:
-500 + -11t + 4t2 = 0

Solving
-500 + -11t + 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'.
-125 + -2.75t + t2 = 0

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + -2.75t + 125 + t2 = 0 + 125

Reorder the terms:
-125 + 125 + -2.75t + t2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + -2.75t + t2 = 0 + 125
-2.75t + t2 = 0 + 125

Combine like terms: 0 + 125 = 125
-2.75t + t2 = 125

The t term is -2.75t.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75t + 1.890625 + t2 = 125 + 1.890625

Reorder the terms:
1.890625 + -2.75t + t2 = 125 + 1.890625

Combine like terms: 125 + 1.890625 = 126.890625
1.890625 + -2.75t + t2 = 126.890625

Factor a perfect square on the left side:
(t + -1.375)(t + -1.375) = 126.890625

Calculate the square root of the right side: 11.264573893

Break this problem into two subproblems by setting 
(t + -1.375) equal to 11.264573893 and -11.264573893.

Subproblem 1

t + -1.375 = 11.264573893 Simplifying t + -1.375 = 11.264573893 Reorder the terms: -1.375 + t = 11.264573893 Solving -1.375 + t = 11.264573893 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + t = 11.264573893 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = 11.264573893 + 1.375 t = 11.264573893 + 1.375 Combine like terms: 11.264573893 + 1.375 = 12.639573893 t = 12.639573893 Simplifying t = 12.639573893

Subproblem 2

t + -1.375 = -11.264573893 Simplifying t + -1.375 = -11.264573893 Reorder the terms: -1.375 + t = -11.264573893 Solving -1.375 + t = -11.264573893 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + t = -11.264573893 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = -11.264573893 + 1.375 t = -11.264573893 + 1.375 Combine like terms: -11.264573893 + 1.375 = -9.889573893 t = -9.889573893 Simplifying t = -9.889573893

Solution

The solution to the problem is based on the solutions from the subproblems. t = {12.639573893, -9.889573893}

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