Solve 25(x^2+1)15=48

$$25 ( x ^ { 2 } + 1 ) 15 = 48$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{545}i}{25}\approx -0-0.933809402i$$

$$x=\frac{\sqrt{545}i}{25}\approx 0.933809402i$$

Steps by Finding Square Root

Multiply 25 and 15 to get 375.

$$375\left(x^{2}+1\right)=48$$

Use the distributive property to multiply 375 by x^{2}+1.

$$375x^{2}+375=48$$

Subtract 375 from both sides.

$$375x^{2}=48-375$$

Subtract 375 from 48 to get -327.

$$375x^{2}=-327$$

Divide both sides by 375.

$$x^{2}=\frac{-327}{375}$$

Reduce the fraction \frac{-327}{375} to lowest terms by extracting and canceling out 3.

$$x^{2}=-\frac{109}{125}$$

The equation is now solved.

$$x=\frac{\sqrt{545}i}{25} x=-\frac{\sqrt{545}i}{25}$$

Steps Using the Quadratic Formula

Multiply 25 and 15 to get 375.

$$375\left(x^{2}+1\right)=48$$

Use the distributive property to multiply 375 by x^{2}+1.

$$375x^{2}+375=48$$

Subtract 48 from both sides.

$$375x^{2}+375-48=0$$

Subtract 48 from 375 to get 327.

$$375x^{2}+327=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 375 for a, 0 for b, and 327 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 375\times 327}}{2\times 375}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 375\times 327}}{2\times 375}$$

Multiply -4 times 375.

$$x=\frac{0±\sqrt{-1500\times 327}}{2\times 375}$$

Multiply -1500 times 327.

$$x=\frac{0±\sqrt{-490500}}{2\times 375}$$

Take the square root of -490500.

$$x=\frac{0±30\sqrt{545}i}{2\times 375}$$

Multiply 2 times 375.

$$x=\frac{0±30\sqrt{545}i}{750}$$

Now solve the equation x=\frac{0±30\sqrt{545}i}{750} when ± is plus.

$$x=\frac{\sqrt{545}i}{25}$$

Now solve the equation x=\frac{0±30\sqrt{545}i}{750} when ± is minus.

$$x=-\frac{\sqrt{545}i}{25}$$

The equation is now solved.

$$x=\frac{\sqrt{545}i}{25} x=-\frac{\sqrt{545}i}{25}$$