Solve (x+7)(x-7)-left(x+2right)^2=5(x-2)+(x-7)

$$(x+7)(x-7)- { \left(x+2 \right) }^{ 2 } =5(x-2)+(x-7)$$

Solve for x

$$x = -\frac{18}{5} = -3\frac{3}{5} = -3.6$$

Steps for Solving Linear Equation

Consider \left(x+7\right)\left(x-7\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 7.

$$x^{2}-49-\left(x+2\right)^{2}=5\left(x-2\right)+x-7$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

$$x^{2}-49-\left(x^{2}+4x+4\right)=5\left(x-2\right)+x-7$$

To find the opposite of x^{2}+4x+4, find the opposite of each term.

$$x^{2}-49-x^{2}-4x-4=5\left(x-2\right)+x-7$$

Combine x^{2} and -x^{2} to get 0.

$$-49-4x-4=5\left(x-2\right)+x-7$$

Subtract 4 from -49 to get -53.

$$-53-4x=5\left(x-2\right)+x-7$$

Use the distributive property to multiply 5 by x-2.

$$-53-4x=5x-10+x-7$$

Combine 5x and x to get 6x.

$$-53-4x=6x-10-7$$

Subtract 7 from -10 to get -17.

$$-53-4x=6x-17$$

Subtract 6x from both sides.

$$-53-4x-6x=-17$$

Combine -4x and -6x to get -10x.

$$-53-10x=-17$$

Add 53 to both sides.

$$-10x=-17+53$$

Add -17 and 53 to get 36.

$$-10x=36$$

Divide both sides by -10.

$$x=\frac{36}{-10}$$

Reduce the fraction \frac{36}{-10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{18}{5}$$