Solve 2025=x^2

$$2025= { x }^{ 2 }$$

Solve for x

$$x=45$$

$$x=-45$$

Steps Using Difference of Squares

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

$$x^{2}=2025$$

Subtract 2025 from both sides.

$$x^{2}-2025=0$$

Consider x^{2}-2025. Rewrite x^{2}-2025 as x^{2}-45^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-45\right)\left(x+45\right)=0$$

To find equation solutions, solve x-45=0 and x+45=0.

$$x=45 x=-45$$

Steps by Finding Square Root

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

$$x^{2}=2025$$

Take the square root of both sides of the equation.

$$x=45 x=-45$$

Steps Using the Quadratic Formula

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

$$x^{2}=2025$$

Subtract 2025 from both sides.

$$x^{2}-2025=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2025 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2025\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2025\right)}}{2}$$

Multiply -4 times -2025.

$$x=\frac{0±\sqrt{8100}}{2}$$

Take the square root of 8100.

$$x=\frac{0±90}{2}$$

Now solve the equation x=\frac{0±90}{2} when ± is plus. Divide 90 by 2.

$$x=45$$

Now solve the equation x=\frac{0±90}{2} when ± is minus. Divide -90 by 2.

$$x=-45$$

The equation is now solved.

$$x=45 x=-45$$