Solve {l}{x^2+25=x^2+2x+1}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x ^ {2} + 25 = x ^ {2} + 2 x + 1 }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=12$$

Solution Steps

Consider the first equation. Subtract x^{2} from both sides.

$$x^{2}+25-x^{2}=2x+1$$

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

$$25=2x+1$$

Swap sides so that all variable terms are on the left hand side.

$$2x+1=25$$

Subtract 1 from both sides.

$$2x=25-1$$

Subtract 1 from 25 to get 24.

$$2x=24$$

Divide both sides by 2.

$$x=\frac{24}{2}$$

Divide 24 by 2 to get 12.

$$x=12$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=12$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=12$$

The system is now solved.

$$x=12 y=12 z=12$$