Solve F=(5x-2)(5x-8)-(3x-5)(x+7)

$$F = ( 5 x - 2 ) ( 5 x - 8 ) - ( 3 x - 5 ) ( x + 7 )$$

Solve for F

$$F=22x^{2}-66x+51$$

Solution Steps

Use the distributive property to multiply 5x-2 by 5x-8 and combine like terms.

$$F=25x^{2}-50x+16-\left(3x-5\right)\left(x+7\right)$$

Use the distributive property to multiply 3x-5 by x+7 and combine like terms.

$$F=25x^{2}-50x+16-\left(3x^{2}+16x-35\right)$$

To find the opposite of 3x^{2}+16x-35, find the opposite of each term.

$$F=25x^{2}-50x+16-3x^{2}-16x+35$$

Combine 25x^{2} and -3x^{2} to get 22x^{2}.

$$F=22x^{2}-50x+16-16x+35$$

Combine -50x and -16x to get -66x.

$$F=22x^{2}-66x+16+35$$

Add 16 and 35 to get 51.

$$F=22x^{2}-66x+51$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{22F-33}}{22}+\frac{3}{2}$$

$$x=\frac{\sqrt{22F-33}}{22}+\frac{3}{2}$$

Solve for x

$$x=-\frac{\sqrt{22F-33}}{22}+\frac{3}{2}$$

$$x=\frac{\sqrt{22F-33}}{22}+\frac{3}{2}\text{, }F\geq \frac{3}{2}$$