16t^2+27t+10=0

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Solution for 16t^2+27t+10=0 equation:


Simplifying
16t2 + 27t + 10 = 0

Reorder the terms:
10 + 27t + 16t2 = 0

Solving
10 + 27t + 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'.
0.625 + 1.6875t + t2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + 1.6875t + -0.625 + t2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + 1.6875t + t2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + 1.6875t + t2 = 0 + -0.625
1.6875t + t2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
1.6875t + t2 = -0.625

The t term is 1.6875t.  Take half its coefficient (0.84375).
Square it (0.7119140625) and add it to both sides.

Add '0.7119140625' to each side of the equation.
1.6875t + 0.7119140625 + t2 = -0.625 + 0.7119140625

Reorder the terms:
0.7119140625 + 1.6875t + t2 = -0.625 + 0.7119140625

Combine like terms: -0.625 + 0.7119140625 = 0.0869140625
0.7119140625 + 1.6875t + t2 = 0.0869140625

Factor a perfect square on the left side:
(t + 0.84375)(t + 0.84375) = 0.0869140625

Calculate the square root of the right side: 0.29481191

Break this problem into two subproblems by setting 
(t + 0.84375) equal to 0.29481191 and -0.29481191.

Subproblem 1

t + 0.84375 = 0.29481191 Simplifying t + 0.84375 = 0.29481191 Reorder the terms: 0.84375 + t = 0.29481191 Solving 0.84375 + t = 0.29481191 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.84375' to each side of the equation. 0.84375 + -0.84375 + t = 0.29481191 + -0.84375 Combine like terms: 0.84375 + -0.84375 = 0.00000 0.00000 + t = 0.29481191 + -0.84375 t = 0.29481191 + -0.84375 Combine like terms: 0.29481191 + -0.84375 = -0.54893809 t = -0.54893809 Simplifying t = -0.54893809

Subproblem 2

t + 0.84375 = -0.29481191 Simplifying t + 0.84375 = -0.29481191 Reorder the terms: 0.84375 + t = -0.29481191 Solving 0.84375 + t = -0.29481191 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.84375' to each side of the equation. 0.84375 + -0.84375 + t = -0.29481191 + -0.84375 Combine like terms: 0.84375 + -0.84375 = 0.00000 0.00000 + t = -0.29481191 + -0.84375 t = -0.29481191 + -0.84375 Combine like terms: -0.29481191 + -0.84375 = -1.13856191 t = -1.13856191 Simplifying t = -1.13856191

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-0.54893809, -1.13856191}

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