Solve 25-x^2=36-left(5-xright)^2

$$25- { x }^{ 2 } = 36- { \left(5-x \right) }^{ 2 }$$

Solve for x

$$x = \frac{7}{5} = 1\frac{2}{5} = 1.4$$

Steps for Solving Linear Equation

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

$$25-x^{2}=36-\left(25-10x+x^{2}\right)$$

To find the opposite of 25-10x+x^{2}, find the opposite of each term.

$$25-x^{2}=36-25+10x-x^{2}$$

Subtract 25 from 36 to get 11.

$$25-x^{2}=11+10x-x^{2}$$

Subtract 10x from both sides.

$$25-x^{2}-10x=11-x^{2}$$

Add x^{2} to both sides.

$$25-x^{2}-10x+x^{2}=11$$

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

$$25-10x=11$$

Subtract 25 from both sides.

$$-10x=11-25$$

Subtract 25 from 11 to get -14.

$$-10x=-14$$

Divide both sides by -10.

$$x=\frac{-14}{-10}$$

Reduce the fraction \frac{-14}{-10} to lowest terms by extracting and canceling out -2.

$$x=\frac{7}{5}$$