Solve 1.8+y^2=9

$$1.8 + y ^ { 2 } = 9$$

Solve for y

$$y = \frac{6 \sqrt{5}}{5} \approx 2.683281573$$

$$y = -\frac{6 \sqrt{5}}{5} \approx -2.683281573$$

Steps by Finding Square Root

Subtract 1.8 from both sides.

$$y^{2}=9-1.8$$

Subtract 1.8 from 9 to get 7.2.

$$y^{2}=7.2$$

Take the square root of both sides of the equation.

$$y=\frac{6\sqrt{5}}{5} y=-\frac{6\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

Subtract 9 from both sides.

$$1.8+y^{2}-9=0$$

Subtract 9 from 1.8 to get -7.2.

$$-7.2+y^{2}=0$$

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.

$$y^{2}-7.2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -7.2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-7.2\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-7.2\right)}}{2}$$

Multiply -4 times -7.2.

$$y=\frac{0±\sqrt{28.8}}{2}$$

Take the square root of 28.8.

$$y=\frac{0±\frac{12\sqrt{5}}{5}}{2}$$

Now solve the equation y=\frac{0±\frac{12\sqrt{5}}{5}}{2} when ± is plus.

$$y=\frac{6\sqrt{5}}{5}$$

Now solve the equation y=\frac{0±\frac{12\sqrt{5}}{5}}{2} when ± is minus.

$$y=-\frac{6\sqrt{5}}{5}$$

The equation is now solved.

$$y=\frac{6\sqrt{5}}{5} y=-\frac{6\sqrt{5}}{5}$$