Solve xx+1/2=780

$$\frac { x x + 1 } { 2 } = 780$$

Solve for x

$$x=\sqrt{1559}\approx 39.484174045$$

$$x=-\sqrt{1559}\approx -39.484174045$$

Steps by Finding Square Root

Multiply both sides by 2.

$$xx+1=780\times 2$$

Multiply x and x to get x^{2}.

$$x^{2}+1=780\times 2$$

Multiply 780 and 2 to get 1560.

$$x^{2}+1=1560$$

Subtract 1 from both sides.

$$x^{2}=1560-1$$

Subtract 1 from 1560 to get 1559.

$$x^{2}=1559$$

Take the square root of both sides of the equation.

$$x=\sqrt{1559} x=-\sqrt{1559}$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$xx+1=780\times 2$$

Multiply x and x to get x^{2}.

$$x^{2}+1=780\times 2$$

Multiply 780 and 2 to get 1560.

$$x^{2}+1=1560$$

Subtract 1560 from both sides.

$$x^{2}+1-1560=0$$

Subtract 1560 from 1 to get -1559.

$$x^{2}-1559=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1559 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1559\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1559\right)}}{2}$$

Multiply -4 times -1559.

$$x=\frac{0±\sqrt{6236}}{2}$$

Take the square root of 6236.

$$x=\frac{0±2\sqrt{1559}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{1559}}{2} when ± is plus.

$$x=\sqrt{1559}$$

Now solve the equation x=\frac{0±2\sqrt{1559}}{2} when ± is minus.

$$x=-\sqrt{1559}$$

The equation is now solved.

$$x=\sqrt{1559} x=-\sqrt{1559}$$