Solve 8[x(x+5x+8x)]=3000

$$8 [ x ( x + 5 x + 8 x ) ] = 3000$$

Solve for x

$$x = \frac{5 \sqrt{210}}{14} \approx 5.175491695$$

$$x = -\frac{5 \sqrt{210}}{14} \approx -5.175491695$$

Steps by Finding Square Root

Combine x and 5x to get 6x.

$$8x\left(6x+8x\right)=3000$$

Combine 6x and 8x to get 14x.

$$8x\times 14x=3000$$

Multiply 8 and 14 to get 112.

$$112xx=3000$$

Multiply x and x to get x^{2}.

$$112x^{2}=3000$$

Divide both sides by 112.

$$x^{2}=\frac{3000}{112}$$

Reduce the fraction \frac{3000}{112} to lowest terms by extracting and canceling out 8.

$$x^{2}=\frac{375}{14}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{210}}{14} x=-\frac{5\sqrt{210}}{14}$$

Steps Using the Quadratic Formula

Combine x and 5x to get 6x.

$$8x\left(6x+8x\right)=3000$$

Combine 6x and 8x to get 14x.

$$8x\times 14x=3000$$

Multiply 8 and 14 to get 112.

$$112xx=3000$$

Multiply x and x to get x^{2}.

$$112x^{2}=3000$$

Subtract 3000 from both sides.

$$112x^{2}-3000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 112 for a, 0 for b, and -3000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 112\left(-3000\right)}}{2\times 112}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 112\left(-3000\right)}}{2\times 112}$$

Multiply -4 times 112.

$$x=\frac{0±\sqrt{-448\left(-3000\right)}}{2\times 112}$$

Multiply -448 times -3000.

$$x=\frac{0±\sqrt{1344000}}{2\times 112}$$

Take the square root of 1344000.

$$x=\frac{0±80\sqrt{210}}{2\times 112}$$

Multiply 2 times 112.

$$x=\frac{0±80\sqrt{210}}{224}$$

Now solve the equation x=\frac{0±80\sqrt{210}}{224} when ± is plus.

$$x=\frac{5\sqrt{210}}{14}$$

Now solve the equation x=\frac{0±80\sqrt{210}}{224} when ± is minus.

$$x=-\frac{5\sqrt{210}}{14}$$

The equation is now solved.

$$x=\frac{5\sqrt{210}}{14} x=-\frac{5\sqrt{210}}{14}$$