Solve 64*6=25*15(x^2+1)

$$64 \times 6 = 25 \times 15 ( x ^ { 2 } + 1 )$$

Solve for x

$$x=\frac{\sqrt{15}}{25}\approx 0.154919334$$

$$x=-\frac{\sqrt{15}}{25}\approx -0.154919334$$

Steps by Finding Square Root

Multiply 64 and 6 to get 384.

$$384=25\times 15\left(x^{2}+1\right)$$

Multiply 25 and 15 to get 375.

$$384=375\left(x^{2}+1\right)$$

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

$$384=375x^{2}+375$$

Swap sides so that all variable terms are on the left hand side.

$$375x^{2}+375=384$$

Subtract 375 from both sides.

$$375x^{2}=384-375$$

Subtract 375 from 384 to get 9.

$$375x^{2}=9$$

Divide both sides by 375.

$$x^{2}=\frac{9}{375}$$

Reduce the fraction \frac{9}{375} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{3}{125}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{15}}{25} x=-\frac{\sqrt{15}}{25}$$

Steps Using the Quadratic Formula

Multiply 64 and 6 to get 384.

$$384=25\times 15\left(x^{2}+1\right)$$

Multiply 25 and 15 to get 375.

$$384=375\left(x^{2}+1\right)$$

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

$$384=375x^{2}+375$$

Swap sides so that all variable terms are on the left hand side.

$$375x^{2}+375=384$$

Subtract 384 from both sides.

$$375x^{2}+375-384=0$$

Subtract 384 from 375 to get -9.

$$375x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 375 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 375\left(-9\right)}}{2\times 375}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 375\left(-9\right)}}{2\times 375}$$

Multiply -4 times 375.

$$x=\frac{0±\sqrt{-1500\left(-9\right)}}{2\times 375}$$

Multiply -1500 times -9.

$$x=\frac{0±\sqrt{13500}}{2\times 375}$$

Take the square root of 13500.

$$x=\frac{0±30\sqrt{15}}{2\times 375}$$

Multiply 2 times 375.

$$x=\frac{0±30\sqrt{15}}{750}$$

Now solve the equation x=\frac{0±30\sqrt{15}}{750} when ± is plus.

$$x=\frac{\sqrt{15}}{25}$$

Now solve the equation x=\frac{0±30\sqrt{15}}{750} when ± is minus.

$$x=-\frac{\sqrt{15}}{25}$$

The equation is now solved.

$$x=\frac{\sqrt{15}}{25} x=-\frac{\sqrt{15}}{25}$$