-16t^2+5t+15=0

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Solution for -16t^2+5t+15=0 equation:


Simplifying
-16t2 + 5t + 15 = 0

Reorder the terms:
15 + 5t + -16t2 = 0

Solving
15 + 5t + -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'.
-0.9375 + -0.3125t + t2 = 0

Move the constant term to the right:

Add '0.9375' to each side of the equation.
-0.9375 + -0.3125t + 0.9375 + t2 = 0 + 0.9375

Reorder the terms:
-0.9375 + 0.9375 + -0.3125t + t2 = 0 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + -0.3125t + t2 = 0 + 0.9375
-0.3125t + t2 = 0 + 0.9375

Combine like terms: 0 + 0.9375 = 0.9375
-0.3125t + t2 = 0.9375

The t term is -0.3125t.  Take half its coefficient (-0.15625).
Square it (0.0244140625) and add it to both sides.

Add '0.0244140625' to each side of the equation.
-0.3125t + 0.0244140625 + t2 = 0.9375 + 0.0244140625

Reorder the terms:
0.0244140625 + -0.3125t + t2 = 0.9375 + 0.0244140625

Combine like terms: 0.9375 + 0.0244140625 = 0.9619140625
0.0244140625 + -0.3125t + t2 = 0.9619140625

Factor a perfect square on the left side:
(t + -0.15625)(t + -0.15625) = 0.9619140625

Calculate the square root of the right side: 0.980772177

Break this problem into two subproblems by setting 
(t + -0.15625) equal to 0.980772177 and -0.980772177.

Subproblem 1

t + -0.15625 = 0.980772177 Simplifying t + -0.15625 = 0.980772177 Reorder the terms: -0.15625 + t = 0.980772177 Solving -0.15625 + t = 0.980772177 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = 0.980772177 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = 0.980772177 + 0.15625 t = 0.980772177 + 0.15625 Combine like terms: 0.980772177 + 0.15625 = 1.137022177 t = 1.137022177 Simplifying t = 1.137022177

Subproblem 2

t + -0.15625 = -0.980772177 Simplifying t + -0.15625 = -0.980772177 Reorder the terms: -0.15625 + t = -0.980772177 Solving -0.15625 + t = -0.980772177 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = -0.980772177 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = -0.980772177 + 0.15625 t = -0.980772177 + 0.15625 Combine like terms: -0.980772177 + 0.15625 = -0.824522177 t = -0.824522177 Simplifying t = -0.824522177

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.137022177, -0.824522177}

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