Solve x^2=1.21

$${ x }^{ 2 } = 1.21$$

Solve for x

$$x=1.1$$

$$x=-1.1$$

Steps Using Difference of Squares

Subtract 1.21 from both sides.

$$x^{2}-1.21=0$$

Consider x^{2}-1.21. Rewrite x^{2}-1.21 as x^{2}-\left(\frac{11}{10}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-\frac{11}{10}\right)\left(x+\frac{11}{10}\right)=0$$

To find equation solutions, solve x-\frac{11}{10}=0 and x+\frac{11}{10}=0.

$$x=\frac{11}{10} x=-\frac{11}{10}$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{11}{10} x=-\frac{11}{10}$$

Steps Using the Quadratic Formula

Subtract 1.21 from both sides.

$$x^{2}-1.21=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1.21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1.21\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1.21\right)}}{2}$$

Multiply -4 times -1.21.

$$x=\frac{0±\sqrt{4.84}}{2}$$

Take the square root of 4.84.

$$x=\frac{0±\frac{11}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{11}{5}}{2} when ± is plus.

$$x=\frac{11}{10}$$

Now solve the equation x=\frac{0±\frac{11}{5}}{2} when ± is minus.

$$x=-\frac{11}{10}$$

The equation is now solved.

$$x=\frac{11}{10} x=-\frac{11}{10}$$