Solve 21x^2+20x^2=9

$$21 { x }^{ 2 } +20 { x }^{ 2 } =9$$

Solve for x

$$x=\frac{3\sqrt{41}}{41}\approx 0.468521286$$

$$x=-\frac{3\sqrt{41}}{41}\approx -0.468521286$$

Steps by Finding Square Root

Combine 21x^{2} and 20x^{2} to get 41x^{2}.

$$41x^{2}=9$$

Divide both sides by 41.

$$x^{2}=\frac{9}{41}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{41}}{41} x=-\frac{3\sqrt{41}}{41}$$

Steps Using the Quadratic Formula

Combine 21x^{2} and 20x^{2} to get 41x^{2}.

$$41x^{2}=9$$

Subtract 9 from both sides.

$$41x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 41 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 41\left(-9\right)}}{2\times 41}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 41\left(-9\right)}}{2\times 41}$$

Multiply -4 times 41.

$$x=\frac{0±\sqrt{-164\left(-9\right)}}{2\times 41}$$

Multiply -164 times -9.

$$x=\frac{0±\sqrt{1476}}{2\times 41}$$

Take the square root of 1476.

$$x=\frac{0±6\sqrt{41}}{2\times 41}$$

Multiply 2 times 41.

$$x=\frac{0±6\sqrt{41}}{82}$$

Now solve the equation x=\frac{0±6\sqrt{41}}{82} when ± is plus.

$$x=\frac{3\sqrt{41}}{41}$$

Now solve the equation x=\frac{0±6\sqrt{41}}{82} when ± is minus.

$$x=-\frac{3\sqrt{41}}{41}$$

The equation is now solved.

$$x=\frac{3\sqrt{41}}{41} x=-\frac{3\sqrt{41}}{41}$$