Solve 21x^2-738x^2+81=1

$$21 x ^ { 2 } - 738 x ^ { 2 } + 81 = 1$$

Solve for x

$$x=\frac{4\sqrt{3585}}{717}\approx 0.334029955$$

$$x=-\frac{4\sqrt{3585}}{717}\approx -0.334029955$$

Steps by Finding Square Root

Combine 21x^{2} and -738x^{2} to get -717x^{2}.

$$-717x^{2}+81=1$$

Subtract 81 from both sides.

$$-717x^{2}=1-81$$

Subtract 81 from 1 to get -80.

$$-717x^{2}=-80$$

Divide both sides by -717.

$$x^{2}=\frac{-80}{-717}$$

Fraction \frac{-80}{-717} can be simplified to \frac{80}{717} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{80}{717}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{3585}}{717} x=-\frac{4\sqrt{3585}}{717}$$

Steps Using the Quadratic Formula

Combine 21x^{2} and -738x^{2} to get -717x^{2}.

$$-717x^{2}+81=1$$

Subtract 1 from both sides.

$$-717x^{2}+81-1=0$$

Subtract 1 from 81 to get 80.

$$-717x^{2}+80=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -717 for a, 0 for b, and 80 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-717\right)\times 80}}{2\left(-717\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-717\right)\times 80}}{2\left(-717\right)}$$

Multiply -4 times -717.

$$x=\frac{0±\sqrt{2868\times 80}}{2\left(-717\right)}$$

Multiply 2868 times 80.

$$x=\frac{0±\sqrt{229440}}{2\left(-717\right)}$$

Take the square root of 229440.

$$x=\frac{0±8\sqrt{3585}}{2\left(-717\right)}$$

Multiply 2 times -717.

$$x=\frac{0±8\sqrt{3585}}{-1434}$$

Now solve the equation x=\frac{0±8\sqrt{3585}}{-1434} when ± is plus.

$$x=-\frac{4\sqrt{3585}}{717}$$

Now solve the equation x=\frac{0±8\sqrt{3585}}{-1434} when ± is minus.

$$x=\frac{4\sqrt{3585}}{717}$$

The equation is now solved.

$$x=-\frac{4\sqrt{3585}}{717} x=\frac{4\sqrt{3585}}{717}$$