Solve x^2=7744

$$x ^ { 2 } = 7744$$

Solve for x

$$x=88$$

$$x=-88$$

Steps Using Difference of Squares

Subtract 7744 from both sides.

$$x^{2}-7744=0$$

Consider x^{2}-7744. Rewrite x^{2}-7744 as x^{2}-88^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-88\right)\left(x+88\right)=0$$

To find equation solutions, solve x-88=0 and x+88=0.

$$x=88 x=-88$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=88 x=-88$$

Steps Using the Quadratic Formula

Subtract 7744 from both sides.

$$x^{2}-7744=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -7744 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-7744\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-7744\right)}}{2}$$

Multiply -4 times -7744.

$$x=\frac{0±\sqrt{30976}}{2}$$

Take the square root of 30976.

$$x=\frac{0±176}{2}$$

Now solve the equation x=\frac{0±176}{2} when ± is plus. Divide 176 by 2.

$$x=88$$

Now solve the equation x=\frac{0±176}{2} when ± is minus. Divide -176 by 2.

$$x=-88$$

The equation is now solved.

$$x=88 x=-88$$