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Expression simplification/ Factor perfect squares/ 4*t^2-5*t-14

Factor 4*t^2-5*t-14 squared

An expression to simplify:

The solution

You have entered [src] 
   2           
4*t  - 5*t - 14
$$\left(4 t^{2} - 5 t\right) - 14$$ 
4*t^2 - 5*t - 14
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(4 t^{2} - 5 t\right) - 14$$
To do this, let's use the formula
$$a t^{2} + b t + c = a \left(m + t\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 4$$
$$b = -5$$
$$c = -14$$
Then
$$m = - \frac{5}{8}$$
$$n = - \frac{249}{16}$$
So,
$$4 \left(t - \frac{5}{8}\right)^{2} - \frac{249}{16}$$
Factorization [src] 
/            _____\ /            _____\
|      5   \/ 249 | |      5   \/ 249 |
|t + - - + -------|*|t + - - - -------|
\      8      8   / \      8      8   /
$$\left(t + \left(- \frac{5}{8} + \frac{\sqrt{249}}{8}\right)\right) \left(t + \left(- \frac{\sqrt{249}}{8} - \frac{5}{8}\right)\right)$$ 
(t - 5/8 + sqrt(249)/8)*(t - 5/8 - sqrt(249)/8)
General simplification [src] 
               2
-14 - 5*t + 4*t
$$4 t^{2} - 5 t - 14$$ 
-14 - 5*t + 4*t^2
Trigonometric part [src] 
               2
-14 - 5*t + 4*t
$$4 t^{2} - 5 t - 14$$ 
-14 - 5*t + 4*t^2
Powers [src] 
               2
-14 - 5*t + 4*t
$$4 t^{2} - 5 t - 14$$ 
-14 - 5*t + 4*t^2
Rational denominator [src] 
               2
-14 - 5*t + 4*t
$$4 t^{2} - 5 t - 14$$ 
-14 - 5*t + 4*t^2
Numerical answer [src] 
-14.0 + 4.0*t^2 - 5.0*t
-14.0 + 4.0*t^2 - 5.0*t
Combining rational expressions [src] 
-14 + t*(-5 + 4*t)
$$t \left(4 t - 5\right) - 14$$ 
-14 + t*(-5 + 4*t)
Common denominator [src] 
               2
-14 - 5*t + 4*t
$$4 t^{2} - 5 t - 14$$ 
-14 - 5*t + 4*t^2
Assemble expression [src] 
               2
-14 - 5*t + 4*t
$$4 t^{2} - 5 t - 14$$ 
-14 - 5*t + 4*t^2
Combinatorics [src] 
               2
-14 - 5*t + 4*t
$$4 t^{2} - 5 t - 14$$ 
-14 - 5*t + 4*t^2
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