Solve (9-9/2-x)^2=x^2+(9-1)^2

$$( 9 - \frac { 9 } { 2 } - x ) ^ { 2 } = x ^ { 2 } + ( 9 - 1 ) ^ { 2 }$$

Solve for x

$$x = -\frac{175}{36} = -4\frac{31}{36} \approx -4.861111111$$

Steps for Solving Linear Equation

Subtract \frac{9}{2} from 9 to get \frac{9}{2}.

$$\left(\frac{9}{2}-x\right)^{2}=x^{2}+\left(9-1\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{9}{2}-x\right)^{2}.

$$\frac{81}{4}-9x+x^{2}=x^{2}+\left(9-1\right)^{2}$$

Subtract 1 from 9 to get 8.

$$\frac{81}{4}-9x+x^{2}=x^{2}+8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{81}{4}-9x+x^{2}=x^{2}+64$$

Subtract x^{2} from both sides.

$$\frac{81}{4}-9x+x^{2}-x^{2}=64$$

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

$$\frac{81}{4}-9x=64$$

Subtract \frac{81}{4} from both sides.

$$-9x=64-\frac{81}{4}$$

Subtract \frac{81}{4} from 64 to get \frac{175}{4}.

$$-9x=\frac{175}{4}$$

Divide both sides by -9.

$$x=\frac{\frac{175}{4}}{-9}$$

Express \frac{\frac{175}{4}}{-9} as a single fraction.

$$x=\frac{175}{4\left(-9\right)}$$

Multiply 4 and -9 to get -36.

$$x=\frac{175}{-36}$$

Fraction \frac{175}{-36} can be rewritten as -\frac{175}{36} by extracting the negative sign.

$$x=-\frac{175}{36}$$