Solve 36-x^2=25-(7-x)(7-x)

$$36- { x }^{ 2 } =25-(7-x)(7-x)$$

Solve for x

$$x = \frac{30}{7} = 4\frac{2}{7} \approx 4.285714286$$

Steps for Solving Linear Equation

Multiply 7-x and 7-x to get \left(7-x\right)^{2}.

$$36-x^{2}=25-\left(7-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7-x\right)^{2}.

$$36-x^{2}=25-\left(49-14x+x^{2}\right)$$

To find the opposite of 49-14x+x^{2}, find the opposite of each term.

$$36-x^{2}=25-49+14x-x^{2}$$

Subtract 49 from 25 to get -24.

$$36-x^{2}=-24+14x-x^{2}$$

Subtract 14x from both sides.

$$36-x^{2}-14x=-24-x^{2}$$

Add x^{2} to both sides.

$$36-x^{2}-14x+x^{2}=-24$$

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

$$36-14x=-24$$

Subtract 36 from both sides.

$$-14x=-24-36$$

Subtract 36 from -24 to get -60.

$$-14x=-60$$

Divide both sides by -14.

$$x=\frac{-60}{-14}$$

Reduce the fraction \frac{-60}{-14} to lowest terms by extracting and canceling out -2.

$$x=\frac{30}{7}$$