16t^2+31t+14=0

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Solution for 16t^2+31t+14=0 equation:


Simplifying
16t2 + 31t + 14 = 0

Reorder the terms:
14 + 31t + 16t2 = 0

Solving
14 + 31t + 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'.
0.875 + 1.9375t + t2 = 0

Move the constant term to the right:

Add '-0.875' to each side of the equation.
0.875 + 1.9375t + -0.875 + t2 = 0 + -0.875

Reorder the terms:
0.875 + -0.875 + 1.9375t + t2 = 0 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + 1.9375t + t2 = 0 + -0.875
1.9375t + t2 = 0 + -0.875

Combine like terms: 0 + -0.875 = -0.875
1.9375t + t2 = -0.875

The t term is 1.9375t.  Take half its coefficient (0.96875).
Square it (0.9384765625) and add it to both sides.

Add '0.9384765625' to each side of the equation.
1.9375t + 0.9384765625 + t2 = -0.875 + 0.9384765625

Reorder the terms:
0.9384765625 + 1.9375t + t2 = -0.875 + 0.9384765625

Combine like terms: -0.875 + 0.9384765625 = 0.0634765625
0.9384765625 + 1.9375t + t2 = 0.0634765625

Factor a perfect square on the left side:
(t + 0.96875)(t + 0.96875) = 0.0634765625

Calculate the square root of the right side: 0.251945555

Break this problem into two subproblems by setting 
(t + 0.96875) equal to 0.251945555 and -0.251945555.

Subproblem 1

t + 0.96875 = 0.251945555 Simplifying t + 0.96875 = 0.251945555 Reorder the terms: 0.96875 + t = 0.251945555 Solving 0.96875 + t = 0.251945555 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.96875' to each side of the equation. 0.96875 + -0.96875 + t = 0.251945555 + -0.96875 Combine like terms: 0.96875 + -0.96875 = 0.00000 0.00000 + t = 0.251945555 + -0.96875 t = 0.251945555 + -0.96875 Combine like terms: 0.251945555 + -0.96875 = -0.716804445 t = -0.716804445 Simplifying t = -0.716804445

Subproblem 2

t + 0.96875 = -0.251945555 Simplifying t + 0.96875 = -0.251945555 Reorder the terms: 0.96875 + t = -0.251945555 Solving 0.96875 + t = -0.251945555 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.96875' to each side of the equation. 0.96875 + -0.96875 + t = -0.251945555 + -0.96875 Combine like terms: 0.96875 + -0.96875 = 0.00000 0.00000 + t = -0.251945555 + -0.96875 t = -0.251945555 + -0.96875 Combine like terms: -0.251945555 + -0.96875 = -1.220695555 t = -1.220695555 Simplifying t = -1.220695555

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-0.716804445, -1.220695555}

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