Solve 36x^2-(5-6x)^2=125

$$36 x ^ { 2 } - ( 5 - 6 x ) ^ { 2 } = 125$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-6x\right)^{2}.

$$36x^{2}-\left(25-60x+36x^{2}\right)=125$$

To find the opposite of 25-60x+36x^{2}, find the opposite of each term.

$$36x^{2}-25+60x-36x^{2}=125$$

Combine 36x^{2} and -36x^{2} to get 0.

$$-25+60x=125$$

Add 25 to both sides.

$$60x=125+25$$

Add 125 and 25 to get 150.

$$60x=150$$

Divide both sides by 60.

$$x=\frac{150}{60}$$

Reduce the fraction \frac{150}{60} to lowest terms by extracting and canceling out 30.

$$x=\frac{5}{2}$$