Solve 4x^2+9/(4-x^2)(1-x^2)=50

$$\frac{ 4 { x }^{ 2 } +9 }{ (4- { x }^{ 2 } )(1- { x }^{ 2 } ) } =50$$

Solve for x

$$x = -\frac{\sqrt{6 \sqrt{731} + 254}}{10} \approx -2.040152127$$

$$x = \frac{\sqrt{6 \sqrt{731} + 254}}{10} \approx 2.040152127$$

$$x=\frac{\sqrt{254-6\sqrt{731}}}{10}\approx 0.958007985$$

$$x=-\frac{\sqrt{254-6\sqrt{731}}}{10}\approx -0.958007985$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -2,-1,1,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x-1\right)\left(x+1\right)\left(x+2\right).

$$4x^{2}+9=50\left(x-2\right)\left(x-1\right)\left(x+1\right)\left(x+2\right)$$

Use the distributive property to multiply 50 by x-2.

$$4x^{2}+9=\left(50x-100\right)\left(x-1\right)\left(x+1\right)\left(x+2\right)$$

Use the distributive property to multiply 50x-100 by x-1 and combine like terms.

$$4x^{2}+9=\left(50x^{2}-150x+100\right)\left(x+1\right)\left(x+2\right)$$

Use the distributive property to multiply 50x^{2}-150x+100 by x+1 and combine like terms.

$$4x^{2}+9=\left(50x^{3}-100x^{2}-50x+100\right)\left(x+2\right)$$

Use the distributive property to multiply 50x^{3}-100x^{2}-50x+100 by x+2 and combine like terms.

$$4x^{2}+9=50x^{4}-250x^{2}+200$$

Subtract 50x^{4} from both sides.

$$4x^{2}+9-50x^{4}=-250x^{2}+200$$

Add 250x^{2} to both sides.

$$4x^{2}+9-50x^{4}+250x^{2}=200$$

Combine 4x^{2} and 250x^{2} to get 254x^{2}.

$$254x^{2}+9-50x^{4}=200$$

Subtract 200 from both sides.

$$254x^{2}+9-50x^{4}-200=0$$

Subtract 200 from 9 to get -191.

$$254x^{2}-191-50x^{4}=0$$

Substitute t for x^{2}.

$$-50t^{2}+254t-191=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute -50 for a, 254 for b, and -191 for c in the quadratic formula.

$$t=\frac{-254±\sqrt{254^{2}-4\left(-50\right)\left(-191\right)}}{-50\times 2}$$

Do the calculations.

$$t=\frac{-254±6\sqrt{731}}{-100}$$

Solve the equation t=\frac{-254±6\sqrt{731}}{-100} when ± is plus and when ± is minus.

$$t=\frac{127-3\sqrt{731}}{50} t=\frac{3\sqrt{731}+127}{50}$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.

$$x=\frac{\sqrt{254-6\sqrt{731}}}{10} x=-\frac{\sqrt{254-6\sqrt{731}}}{10} x=\frac{\sqrt{6\sqrt{731}+254}}{10} x=-\frac{\sqrt{6\sqrt{731}+254}}{10}$$