Solve 4-y^2=1

$$4- { y }^{ 2 } =1$$

Solve for y

$$y=\sqrt{3}\approx 1.732050808$$

$$y=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$-y^{2}=1-4$$

Subtract 4 from 1 to get -3.

$$-y^{2}=-3$$

Divide both sides by -1.

$$y^{2}=\frac{-3}{-1}$$

Fraction \frac{-3}{-1} can be simplified to 3 by removing the negative sign from both the numerator and the denominator.

$$y^{2}=3$$

Take the square root of both sides of the equation.

$$y=\sqrt{3} y=-\sqrt{3}$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$4-y^{2}-1=0$$

Subtract 1 from 4 to get 3.

$$3-y^{2}=0$$

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.

$$-y^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$y=\frac{0±\sqrt{4\times 3}}{2\left(-1\right)}$$

Multiply 4 times 3.

$$y=\frac{0±\sqrt{12}}{2\left(-1\right)}$$

Take the square root of 12.

$$y=\frac{0±2\sqrt{3}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$y=\frac{0±2\sqrt{3}}{-2}$$

Now solve the equation y=\frac{0±2\sqrt{3}}{-2} when ± is plus.

$$y=-\sqrt{3}$$

Now solve the equation y=\frac{0±2\sqrt{3}}{-2} when ± is minus.

$$y=\sqrt{3}$$

The equation is now solved.

$$y=-\sqrt{3} y=\sqrt{3}$$