Solve 5x^2-9=46

$$5 { x }^{ 2 } -9 = 46$$

Solve for x

$$x=\sqrt{11}\approx 3.31662479$$

$$x=-\sqrt{11}\approx -3.31662479$$

Steps by Finding Square Root

Add 9 to both sides.

$$5x^{2}=46+9$$

Add 46 and 9 to get 55.

$$5x^{2}=55$$

Divide both sides by 5.

$$x^{2}=\frac{55}{5}$$

Divide 55 by 5 to get 11.

$$x^{2}=11$$

Take the square root of both sides of the equation.

$$x=\sqrt{11} x=-\sqrt{11}$$

Steps Using the Quadratic Formula

Subtract 46 from both sides.

$$5x^{2}-9-46=0$$

Subtract 46 from -9 to get -55.

$$5x^{2}-55=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -55 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-55\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-55\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-55\right)}}{2\times 5}$$

Multiply -20 times -55.

$$x=\frac{0±\sqrt{1100}}{2\times 5}$$

Take the square root of 1100.

$$x=\frac{0±10\sqrt{11}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±10\sqrt{11}}{10}$$

Now solve the equation x=\frac{0±10\sqrt{11}}{10} when ± is plus.

$$x=\sqrt{11}$$

Now solve the equation x=\frac{0±10\sqrt{11}}{10} when ± is minus.

$$x=-\sqrt{11}$$

The equation is now solved.

$$x=\sqrt{11} x=-\sqrt{11}$$