Solve 77/7x=x+7x

$$\frac{ 77 }{ 7x } =x+7x$$

Solve for x

$$x = \frac{\sqrt{22}}{4} \approx 1.17260394$$

$$x = -\frac{\sqrt{22}}{4} \approx -1.17260394$$

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 7x.

$$77=7xx+7x\times 7x$$

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

$$77=7x^{2}+7x\times 7x$$

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

$$77=7x^{2}+7x^{2}\times 7$$

Multiply 7 and 7 to get 49.

$$77=7x^{2}+49x^{2}$$

Combine 7x^{2} and 49x^{2} to get 56x^{2}.

$$77=56x^{2}$$

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

$$56x^{2}=77$$

Divide both sides by 56.

$$x^{2}=\frac{77}{56}$$

Reduce the fraction \frac{77}{56} to lowest terms by extracting and canceling out 7.

$$x^{2}=\frac{11}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{22}}{4} x=-\frac{\sqrt{22}}{4}$$

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 7x.

$$77=7xx+7x\times 7x$$

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

$$77=7x^{2}+7x\times 7x$$

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

$$77=7x^{2}+7x^{2}\times 7$$

Multiply 7 and 7 to get 49.

$$77=7x^{2}+49x^{2}$$

Combine 7x^{2} and 49x^{2} to get 56x^{2}.

$$77=56x^{2}$$

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

$$56x^{2}=77$$

Subtract 77 from both sides.

$$56x^{2}-77=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 56 for a, 0 for b, and -77 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 56\left(-77\right)}}{2\times 56}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 56\left(-77\right)}}{2\times 56}$$

Multiply -4 times 56.

$$x=\frac{0±\sqrt{-224\left(-77\right)}}{2\times 56}$$

Multiply -224 times -77.

$$x=\frac{0±\sqrt{17248}}{2\times 56}$$

Take the square root of 17248.

$$x=\frac{0±28\sqrt{22}}{2\times 56}$$

Multiply 2 times 56.

$$x=\frac{0±28\sqrt{22}}{112}$$

Now solve the equation x=\frac{0±28\sqrt{22}}{112} when ± is plus.

$$x=\frac{\sqrt{22}}{4}$$

Now solve the equation x=\frac{0±28\sqrt{22}}{112} when ± is minus.

$$x=-\frac{\sqrt{22}}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{22}}{4} x=-\frac{\sqrt{22}}{4}$$