.79=10t-16t^2

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Solution for .79=10t-16t^2 equation:


Simplifying
0.79 = 10t + -16t2

Solving
0.79 = 10t + -16t2

Solving for variable 't'.

Reorder the terms:
0.79 + -10t + 16t2 = 10t + -10t + -16t2 + 16t2

Combine like terms: 10t + -10t = 0
0.79 + -10t + 16t2 = 0 + -16t2 + 16t2
0.79 + -10t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
0.79 + -10t + 16t2 = 0

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

Divide each side by '16'.
0.049375 + -0.625t + t2 = 0

Move the constant term to the right:

Add '-0.049375' to each side of the equation.
0.049375 + -0.625t + -0.049375 + t2 = 0 + -0.049375

Reorder the terms:
0.049375 + -0.049375 + -0.625t + t2 = 0 + -0.049375

Combine like terms: 0.049375 + -0.049375 = 0.000000
0.000000 + -0.625t + t2 = 0 + -0.049375
-0.625t + t2 = 0 + -0.049375

Combine like terms: 0 + -0.049375 = -0.049375
-0.625t + t2 = -0.049375

The t term is -0.625t.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625t + 0.09765625 + t2 = -0.049375 + 0.09765625

Reorder the terms:
0.09765625 + -0.625t + t2 = -0.049375 + 0.09765625

Combine like terms: -0.049375 + 0.09765625 = 0.04828125
0.09765625 + -0.625t + t2 = 0.04828125

Factor a perfect square on the left side:
(t + -0.3125)(t + -0.3125) = 0.04828125

Calculate the square root of the right side: 0.219729948

Break this problem into two subproblems by setting 
(t + -0.3125) equal to 0.219729948 and -0.219729948.

Subproblem 1

t + -0.3125 = 0.219729948 Simplifying t + -0.3125 = 0.219729948 Reorder the terms: -0.3125 + t = 0.219729948 Solving -0.3125 + t = 0.219729948 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = 0.219729948 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = 0.219729948 + 0.3125 t = 0.219729948 + 0.3125 Combine like terms: 0.219729948 + 0.3125 = 0.532229948 t = 0.532229948 Simplifying t = 0.532229948

Subproblem 2

t + -0.3125 = -0.219729948 Simplifying t + -0.3125 = -0.219729948 Reorder the terms: -0.3125 + t = -0.219729948 Solving -0.3125 + t = -0.219729948 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = -0.219729948 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = -0.219729948 + 0.3125 t = -0.219729948 + 0.3125 Combine like terms: -0.219729948 + 0.3125 = 0.092770052 t = 0.092770052 Simplifying t = 0.092770052

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.532229948, 0.092770052}

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