Solve x^2+(3025)^1/2=3899

$$x ^ { 2 } + ( 3025 ) ^ { 1 / 2 } = 3899$$

Solve for x

$$x=-62$$

$$x=62$$

Steps Using Difference of Squares

Calculate 3025 to the power of \frac{1}{2} and get 55.

$$x^{2}+55=3899$$

Subtract 3899 from both sides.

$$x^{2}+55-3899=0$$

Subtract 3899 from 55 to get -3844.

$$x^{2}-3844=0$$

Consider x^{2}-3844. Rewrite x^{2}-3844 as x^{2}-62^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-62\right)\left(x+62\right)=0$$

To find equation solutions, solve x-62=0 and x+62=0.

$$x=62 x=-62$$

Steps by Finding Square Root

Calculate 3025 to the power of \frac{1}{2} and get 55.

$$x^{2}+55=3899$$

Subtract 55 from both sides.

$$x^{2}=3899-55$$

Subtract 55 from 3899 to get 3844.

$$x^{2}=3844$$

Take the square root of both sides of the equation.

$$x=62 x=-62$$

Steps Using the Quadratic Formula

Calculate 3025 to the power of \frac{1}{2} and get 55.

$$x^{2}+55=3899$$

Subtract 3899 from both sides.

$$x^{2}+55-3899=0$$

Subtract 3899 from 55 to get -3844.

$$x^{2}-3844=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3844 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3844\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3844\right)}}{2}$$

Multiply -4 times -3844.

$$x=\frac{0±\sqrt{15376}}{2}$$

Take the square root of 15376.

$$x=\frac{0±124}{2}$$

Now solve the equation x=\frac{0±124}{2} when ± is plus. Divide 124 by 2.

$$x=62$$

Now solve the equation x=\frac{0±124}{2} when ± is minus. Divide -124 by 2.

$$x=-62$$

The equation is now solved.

$$x=62 x=-62$$