Solve 7*8/x+8*7x=x

$$7 \times \frac{ 8 }{ x } +8 \cdot 7x = x$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{770}i}{55}\approx -0-1.009049958i$$

$$x=\frac{2\sqrt{770}i}{55}\approx 1.009049958i$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$7\times 8+8\times 7xx=xx$$

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

$$7\times 8+8\times 7x^{2}=xx$$

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

$$7\times 8+8\times 7x^{2}=x^{2}$$

Multiply 7 and 8 to get 56. Multiply 8 and 7 to get 56.

$$56+56x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$56+56x^{2}-x^{2}=0$$

Combine 56x^{2} and -x^{2} to get 55x^{2}.

$$56+55x^{2}=0$$

Subtract 56 from both sides. Anything subtracted from zero gives its negation.

$$55x^{2}=-56$$

Divide both sides by 55.

$$x^{2}=-\frac{56}{55}$$

The equation is now solved.

$$x=\frac{2\sqrt{770}i}{55} x=-\frac{2\sqrt{770}i}{55}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$7\times 8+8\times 7xx=xx$$

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

$$7\times 8+8\times 7x^{2}=xx$$

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

$$7\times 8+8\times 7x^{2}=x^{2}$$

Multiply 7 and 8 to get 56. Multiply 8 and 7 to get 56.

$$56+56x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$56+56x^{2}-x^{2}=0$$

Combine 56x^{2} and -x^{2} to get 55x^{2}.

$$56+55x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$55x^{2}+56=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 55 for a, 0 for b, and 56 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 55\times 56}}{2\times 55}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 55\times 56}}{2\times 55}$$

Multiply -4 times 55.

$$x=\frac{0±\sqrt{-220\times 56}}{2\times 55}$$

Multiply -220 times 56.

$$x=\frac{0±\sqrt{-12320}}{2\times 55}$$

Take the square root of -12320.

$$x=\frac{0±4\sqrt{770}i}{2\times 55}$$

Multiply 2 times 55.

$$x=\frac{0±4\sqrt{770}i}{110}$$

Now solve the equation x=\frac{0±4\sqrt{770}i}{110} when ± is plus.

$$x=\frac{2\sqrt{770}i}{55}$$

Now solve the equation x=\frac{0±4\sqrt{770}i}{110} when ± is minus.

$$x=-\frac{2\sqrt{770}i}{55}$$

The equation is now solved.

$$x=\frac{2\sqrt{770}i}{55} x=-\frac{2\sqrt{770}i}{55}$$