25=7+35t-16t^2

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Solution for 25=7+35t-16t^2 equation:


Simplifying
25 = 7 + 35t + -16t2

Solving
25 = 7 + 35t + -16t2

Solving for variable 't'.

Combine like terms: 25 + -7 = 18
18 + -35t + 16t2 = 7 + 35t + -16t2 + -7 + -35t + 16t2

Reorder the terms:
18 + -35t + 16t2 = 7 + -7 + 35t + -35t + -16t2 + 16t2

Combine like terms: 7 + -7 = 0
18 + -35t + 16t2 = 0 + 35t + -35t + -16t2 + 16t2
18 + -35t + 16t2 = 35t + -35t + -16t2 + 16t2

Combine like terms: 35t + -35t = 0
18 + -35t + 16t2 = 0 + -16t2 + 16t2
18 + -35t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
18 + -35t + 16t2 = 0

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

Divide each side by '16'.
1.125 + -2.1875t + t2 = 0

Move the constant term to the right:

Add '-1.125' to each side of the equation.
1.125 + -2.1875t + -1.125 + t2 = 0 + -1.125

Reorder the terms:
1.125 + -1.125 + -2.1875t + t2 = 0 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + -2.1875t + t2 = 0 + -1.125
-2.1875t + t2 = 0 + -1.125

Combine like terms: 0 + -1.125 = -1.125
-2.1875t + t2 = -1.125

The t term is -2.1875t.  Take half its coefficient (-1.09375).
Square it (1.196289063) and add it to both sides.

Add '1.196289063' to each side of the equation.
-2.1875t + 1.196289063 + t2 = -1.125 + 1.196289063

Reorder the terms:
1.196289063 + -2.1875t + t2 = -1.125 + 1.196289063

Combine like terms: -1.125 + 1.196289063 = 0.071289063
1.196289063 + -2.1875t + t2 = 0.071289063

Factor a perfect square on the left side:
(t + -1.09375)(t + -1.09375) = 0.071289063

Calculate the square root of the right side: 0.267000118

Break this problem into two subproblems by setting 
(t + -1.09375) equal to 0.267000118 and -0.267000118.

Subproblem 1

t + -1.09375 = 0.267000118 Simplifying t + -1.09375 = 0.267000118 Reorder the terms: -1.09375 + t = 0.267000118 Solving -1.09375 + t = 0.267000118 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + t = 0.267000118 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = 0.267000118 + 1.09375 t = 0.267000118 + 1.09375 Combine like terms: 0.267000118 + 1.09375 = 1.360750118 t = 1.360750118 Simplifying t = 1.360750118

Subproblem 2

t + -1.09375 = -0.267000118 Simplifying t + -1.09375 = -0.267000118 Reorder the terms: -1.09375 + t = -0.267000118 Solving -1.09375 + t = -0.267000118 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + t = -0.267000118 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = -0.267000118 + 1.09375 t = -0.267000118 + 1.09375 Combine like terms: -0.267000118 + 1.09375 = 0.826749882 t = 0.826749882 Simplifying t = 0.826749882

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.360750118, 0.826749882}

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