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Factor 8*x^4-14*x^2-3 squared

An expression to simplify:

The solution

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   4       2    
8*x  - 14*x  - 3
$$\left(8 x^{4} - 14 x^{2}\right) - 3$$
8*x^4 - 14*x^2 - 3
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(8 x^{4} - 14 x^{2}\right) - 3$$
To do this, let's use the formula
$$a x^{4} + b x^{2} + c = a \left(m + x^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 8$$
$$b = -14$$
$$c = -3$$
Then
$$m = - \frac{7}{8}$$
$$n = - \frac{73}{8}$$
So,
$$8 \left(x^{2} - \frac{7}{8}\right)^{2} - \frac{73}{8}$$
General simplification [src]
         2      4
-3 - 14*x  + 8*x 
$$8 x^{4} - 14 x^{2} - 3$$
-3 - 14*x^2 + 8*x^4
Factorization [src]
/           ______________\ /           ______________\ /         ____________\ /         ____________\
|          /         ____ | |          /         ____ | |        /       ____ | |        /       ____ |
|         /    7   \/ 73  | |         /    7   \/ 73  | |       /  7   \/ 73  | |       /  7   \/ 73  |
|x + I*  /   - - + ------ |*|x - I*  /   - - + ------ |*|x +   /   - + ------ |*|x -   /   - + ------ |
\      \/      8     8    / \      \/      8     8    / \    \/    8     8    / \    \/    8     8    /
$$\left(x - i \sqrt{- \frac{7}{8} + \frac{\sqrt{73}}{8}}\right) \left(x + i \sqrt{- \frac{7}{8} + \frac{\sqrt{73}}{8}}\right) \left(x + \sqrt{\frac{7}{8} + \frac{\sqrt{73}}{8}}\right) \left(x - \sqrt{\frac{7}{8} + \frac{\sqrt{73}}{8}}\right)$$
(((x + i*sqrt(-7/8 + sqrt(73)/8))*(x - i*sqrt(-7/8 + sqrt(73)/8)))*(x + sqrt(7/8 + sqrt(73)/8)))*(x - sqrt(7/8 + sqrt(73)/8))
Common denominator [src]
         2      4
-3 - 14*x  + 8*x 
$$8 x^{4} - 14 x^{2} - 3$$
-3 - 14*x^2 + 8*x^4
Trigonometric part [src]
         2      4
-3 - 14*x  + 8*x 
$$8 x^{4} - 14 x^{2} - 3$$
-3 - 14*x^2 + 8*x^4
Assemble expression [src]
         2      4
-3 - 14*x  + 8*x 
$$8 x^{4} - 14 x^{2} - 3$$
-3 - 14*x^2 + 8*x^4
Powers [src]
         2      4
-3 - 14*x  + 8*x 
$$8 x^{4} - 14 x^{2} - 3$$
-3 - 14*x^2 + 8*x^4
Combining rational expressions [src]
        2 /        2\
-3 + 2*x *\-7 + 4*x /
$$2 x^{2} \left(4 x^{2} - 7\right) - 3$$
-3 + 2*x^2*(-7 + 4*x^2)
Numerical answer [src]
-3.0 + 8.0*x^4 - 14.0*x^2
-3.0 + 8.0*x^4 - 14.0*x^2
Rational denominator [src]
         2      4
-3 - 14*x  + 8*x 
$$8 x^{4} - 14 x^{2} - 3$$
-3 - 14*x^2 + 8*x^4
Combinatorics [src]
         2      4
-3 - 14*x  + 8*x 
$$8 x^{4} - 14 x^{2} - 3$$
-3 - 14*x^2 + 8*x^4
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