-16t^2+24t=-5

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Solution for -16t^2+24t=-5 equation:


Simplifying
-16t2 + 24t = -5

Reorder the terms:
24t + -16t2 = -5

Solving
24t + -16t2 = -5

Solving for variable 't'.

Reorder the terms:
5 + 24t + -16t2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 24t + -16t2 = 0

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

Divide each side by '-16'.
-0.3125 + -1.5t + t2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -1.5t + 0.3125 + t2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -1.5t + t2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -1.5t + t2 = 0 + 0.3125
-1.5t + t2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-1.5t + t2 = 0.3125

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = 0.3125 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = 0.3125 + 0.5625

Combine like terms: 0.3125 + 0.5625 = 0.875
0.5625 + -1.5t + t2 = 0.875

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = 0.875

Calculate the square root of the right side: 0.935414347

Break this problem into two subproblems by setting 
(t + -0.75) equal to 0.935414347 and -0.935414347.

Subproblem 1

t + -0.75 = 0.935414347 Simplifying t + -0.75 = 0.935414347 Reorder the terms: -0.75 + t = 0.935414347 Solving -0.75 + t = 0.935414347 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = 0.935414347 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = 0.935414347 + 0.75 t = 0.935414347 + 0.75 Combine like terms: 0.935414347 + 0.75 = 1.685414347 t = 1.685414347 Simplifying t = 1.685414347

Subproblem 2

t + -0.75 = -0.935414347 Simplifying t + -0.75 = -0.935414347 Reorder the terms: -0.75 + t = -0.935414347 Solving -0.75 + t = -0.935414347 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = -0.935414347 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = -0.935414347 + 0.75 t = -0.935414347 + 0.75 Combine like terms: -0.935414347 + 0.75 = -0.185414347 t = -0.185414347 Simplifying t = -0.185414347

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.685414347, -0.185414347}

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