Solve (x+6)^2-(x-5)(x+5)=79

$$( x + 6 ) ^ { 2 } - ( x - 5 ) ( x + 5 ) = 79$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$x^{2}+12x+36-\left(x-5\right)\left(x+5\right)=79$$

Consider \left(x-5\right)\left(x+5\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 5.

$$x^{2}+12x+36-\left(x^{2}-25\right)=79$$

To find the opposite of x^{2}-25, find the opposite of each term.

$$x^{2}+12x+36-x^{2}+25=79$$

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

$$12x+36+25=79$$

Add 36 and 25 to get 61.

$$12x+61=79$$

Subtract 61 from both sides.

$$12x=79-61$$

Subtract 61 from 79 to get 18.

$$12x=18$$

Divide both sides by 12.

$$x=\frac{18}{12}$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

$$x=\frac{3}{2}$$