Solve 3b-(5-x)^2=25-x^2

$$3 b - ( 5 - x ) ^ { 2 } = 25 - x ^ { 2 }$$

Solve for b

$$b=\frac{50-10x}{3}$$

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}.

$$3b-\left(25-10x+x^{2}\right)=25-x^{2}$$

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

$$3b-25+10x-x^{2}=25-x^{2}$$

Add 25 to both sides.

$$3b+10x-x^{2}=25-x^{2}+25$$

Add 25 and 25 to get 50.

$$3b+10x-x^{2}=50-x^{2}$$

Subtract 10x from both sides.

$$3b-x^{2}=50-x^{2}-10x$$

Add x^{2} to both sides.

$$3b=50-x^{2}-10x+x^{2}$$

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

$$3b=50-10x$$

Divide both sides by 3.

$$\frac{3b}{3}=\frac{50-10x}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$b=\frac{50-10x}{3}$$

Solve for x

$$x=-\frac{3b}{10}+5$$

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}.

$$3b-\left(25-10x+x^{2}\right)=25-x^{2}$$

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

$$3b-25+10x-x^{2}=25-x^{2}$$

Add x^{2} to both sides.

$$3b-25+10x-x^{2}+x^{2}=25$$

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

$$3b-25+10x=25$$

Subtract 3b from both sides.

$$-25+10x=25-3b$$

Add 25 to both sides.

$$10x=25-3b+25$$

Add 25 and 25 to get 50.

$$10x=50-3b$$

Divide both sides by 10.

$$\frac{10x}{10}=\frac{50-3b}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$x=\frac{50-3b}{10}$$

Divide 50-3b by 10.

$$x=-\frac{3b}{10}+5$$