Solve 1962^2-y^2=1

$$1962 ^ { 2 } - y ^ { 2 } = 1$$

Solve for y

$$y=\sqrt{3849443}\approx 1961.999745158$$

$$y=-\sqrt{3849443}\approx -1961.999745158$$

Steps by Finding Square Root

Calculate 1962 to the power of 2 and get 3849444.

$$3849444-y^{2}=1$$

Subtract 3849444 from both sides.

$$-y^{2}=1-3849444$$

Subtract 3849444 from 1 to get -3849443.

$$-y^{2}=-3849443$$

Divide both sides by -1.

$$y^{2}=\frac{-3849443}{-1}$$

Fraction \frac{-3849443}{-1} can be simplified to 3849443 by removing the negative sign from both the numerator and the denominator.

$$y^{2}=3849443$$

Take the square root of both sides of the equation.

$$y=\sqrt{3849443} y=-\sqrt{3849443}$$

Steps Using the Quadratic Formula

Calculate 1962 to the power of 2 and get 3849444.

$$3849444-y^{2}=1$$

Subtract 1 from both sides.

$$3849444-y^{2}-1=0$$

Subtract 1 from 3849444 to get 3849443.

$$3849443-y^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-y^{2}+3849443=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 3849443 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 3849443}}{2\left(-1\right)}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-1\right)\times 3849443}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$y=\frac{0±\sqrt{4\times 3849443}}{2\left(-1\right)}$$

Multiply 4 times 3849443.

$$y=\frac{0±\sqrt{15397772}}{2\left(-1\right)}$$

Take the square root of 15397772.

$$y=\frac{0±2\sqrt{3849443}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$y=\frac{0±2\sqrt{3849443}}{-2}$$

Now solve the equation y=\frac{0±2\sqrt{3849443}}{-2} when ± is plus.

$$y=-\sqrt{3849443}$$

Now solve the equation y=\frac{0±2\sqrt{3849443}}{-2} when ± is minus.

$$y=\sqrt{3849443}$$

The equation is now solved.

$$y=-\sqrt{3849443} y=\sqrt{3849443}$$