Solve G=x^2-9-(2x+5)(x-3)+5x-15

$$G = x ^ { 2 } - 9 - ( 2 x + 5 ) ( x - 3 ) + 5 x - 15$$

Solve for G

$$G=-\left(x-3\right)^{2}$$

Solution Steps

Use the distributive property to multiply 2x+5 by x-3 and combine like terms.

$$G=x^{2}-9-\left(2x^{2}-x-15\right)+5x-15$$

To find the opposite of 2x^{2}-x-15, find the opposite of each term.

$$G=x^{2}-9-2x^{2}+x+15+5x-15$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$G=-x^{2}-9+x+15+5x-15$$

Add -9 and 15 to get 6.

$$G=-x^{2}+6+x+5x-15$$

Combine x and 5x to get 6x.

$$G=-x^{2}+6+6x-15$$

Subtract 15 from 6 to get -9.

$$G=-x^{2}-9+6x$$

Solve for x (complex solution)

$$x=-\sqrt{-G}+3$$

$$x=\sqrt{-G}+3$$

Solve for x

$$x=-\sqrt{-G}+3$$

$$x=\sqrt{-G}+3\text{, }G\leq 0$$