Solve x^2+1=226

$$x ^ { 2 } + 1 = 226$$

Solve for x

$$x=15$$

$$x=-15$$

Steps Using Difference of Squares

Subtract 226 from both sides.

$$x^{2}+1-226=0$$

Subtract 226 from 1 to get -225.

$$x^{2}-225=0$$

Consider x^{2}-225. Rewrite x^{2}-225 as x^{2}-15^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-15\right)\left(x+15\right)=0$$

To find equation solutions, solve x-15=0 and x+15=0.

$$x=15 x=-15$$

Steps by Finding Square Root

Subtract 1 from both sides.

$$x^{2}=226-1$$

Subtract 1 from 226 to get 225.

$$x^{2}=225$$

Take the square root of both sides of the equation.

$$x=15 x=-15$$

Steps Using the Quadratic Formula

Subtract 226 from both sides.

$$x^{2}+1-226=0$$

Subtract 226 from 1 to get -225.

$$x^{2}-225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-225\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-225\right)}}{2}$$

Multiply -4 times -225.

$$x=\frac{0±\sqrt{900}}{2}$$

Take the square root of 900.

$$x=\frac{0±30}{2}$$

Now solve the equation x=\frac{0±30}{2} when ± is plus. Divide 30 by 2.

$$x=15$$

Now solve the equation x=\frac{0±30}{2} when ± is minus. Divide -30 by 2.

$$x=-15$$

The equation is now solved.

$$x=15 x=-15$$