0=-8t^2+75t+1800

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Solution for 0=-8t^2+75t+1800 equation:


Simplifying
0 = -8t2 + 75t + 1800

Reorder the terms:
0 = 1800 + 75t + -8t2

Solving
0 = 1800 + 75t + -8t2

Solving for variable 't'.

Combine like terms: 0 + -1800 = -1800
-1800 + -75t + 8t2 = 1800 + 75t + -8t2 + -1800 + -75t + 8t2

Reorder the terms:
-1800 + -75t + 8t2 = 1800 + -1800 + 75t + -75t + -8t2 + 8t2

Combine like terms: 1800 + -1800 = 0
-1800 + -75t + 8t2 = 0 + 75t + -75t + -8t2 + 8t2
-1800 + -75t + 8t2 = 75t + -75t + -8t2 + 8t2

Combine like terms: 75t + -75t = 0
-1800 + -75t + 8t2 = 0 + -8t2 + 8t2
-1800 + -75t + 8t2 = -8t2 + 8t2

Combine like terms: -8t2 + 8t2 = 0
-1800 + -75t + 8t2 = 0

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

Divide each side by '8'.
-225 + -9.375t + t2 = 0

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + -9.375t + 225 + t2 = 0 + 225

Reorder the terms:
-225 + 225 + -9.375t + t2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -9.375t + t2 = 0 + 225
-9.375t + t2 = 0 + 225

Combine like terms: 0 + 225 = 225
-9.375t + t2 = 225

The t term is -9.375t.  Take half its coefficient (-4.6875).
Square it (21.97265625) and add it to both sides.

Add '21.97265625' to each side of the equation.
-9.375t + 21.97265625 + t2 = 225 + 21.97265625

Reorder the terms:
21.97265625 + -9.375t + t2 = 225 + 21.97265625

Combine like terms: 225 + 21.97265625 = 246.97265625
21.97265625 + -9.375t + t2 = 246.97265625

Factor a perfect square on the left side:
(t + -4.6875)(t + -4.6875) = 246.97265625

Calculate the square root of the right side: 15.715363701

Break this problem into two subproblems by setting 
(t + -4.6875) equal to 15.715363701 and -15.715363701.

Subproblem 1

t + -4.6875 = 15.715363701 Simplifying t + -4.6875 = 15.715363701 Reorder the terms: -4.6875 + t = 15.715363701 Solving -4.6875 + t = 15.715363701 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = 15.715363701 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 15.715363701 + 4.6875 t = 15.715363701 + 4.6875 Combine like terms: 15.715363701 + 4.6875 = 20.402863701 t = 20.402863701 Simplifying t = 20.402863701

Subproblem 2

t + -4.6875 = -15.715363701 Simplifying t + -4.6875 = -15.715363701 Reorder the terms: -4.6875 + t = -15.715363701 Solving -4.6875 + t = -15.715363701 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = -15.715363701 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -15.715363701 + 4.6875 t = -15.715363701 + 4.6875 Combine like terms: -15.715363701 + 4.6875 = -11.027863701 t = -11.027863701 Simplifying t = -11.027863701

Solution

The solution to the problem is based on the solutions from the subproblems. t = {20.402863701, -11.027863701}

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