16t^2+25t-112=0

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Solution for 16t^2+25t-112=0 equation:


Simplifying
16t2 + 25t + -112 = 0

Reorder the terms:
-112 + 25t + 16t2 = 0

Solving
-112 + 25t + 16t2 = 0

Solving for variable 't'.

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

Divide each side by '16'.
-7 + 1.5625t + t2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 1.5625t + 7 + t2 = 0 + 7

Reorder the terms:
-7 + 7 + 1.5625t + t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 1.5625t + t2 = 0 + 7
1.5625t + t2 = 0 + 7

Combine like terms: 0 + 7 = 7
1.5625t + t2 = 7

The t term is 1.5625t.  Take half its coefficient (0.78125).
Square it (0.6103515625) and add it to both sides.

Add '0.6103515625' to each side of the equation.
1.5625t + 0.6103515625 + t2 = 7 + 0.6103515625

Reorder the terms:
0.6103515625 + 1.5625t + t2 = 7 + 0.6103515625

Combine like terms: 7 + 0.6103515625 = 7.6103515625
0.6103515625 + 1.5625t + t2 = 7.6103515625

Factor a perfect square on the left side:
(t + 0.78125)(t + 0.78125) = 7.6103515625

Calculate the square root of the right side: 2.758686565

Break this problem into two subproblems by setting 
(t + 0.78125) equal to 2.758686565 and -2.758686565.

Subproblem 1

t + 0.78125 = 2.758686565 Simplifying t + 0.78125 = 2.758686565 Reorder the terms: 0.78125 + t = 2.758686565 Solving 0.78125 + t = 2.758686565 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + t = 2.758686565 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = 2.758686565 + -0.78125 t = 2.758686565 + -0.78125 Combine like terms: 2.758686565 + -0.78125 = 1.977436565 t = 1.977436565 Simplifying t = 1.977436565

Subproblem 2

t + 0.78125 = -2.758686565 Simplifying t + 0.78125 = -2.758686565 Reorder the terms: 0.78125 + t = -2.758686565 Solving 0.78125 + t = -2.758686565 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + t = -2.758686565 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = -2.758686565 + -0.78125 t = -2.758686565 + -0.78125 Combine like terms: -2.758686565 + -0.78125 = -3.539936565 t = -3.539936565 Simplifying t = -3.539936565

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.977436565, -3.539936565}

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