Solve 7^2/x^2-49=1

$$\frac { 7 ^ { 2 } } { x ^ { 2 } - 49 } = 1$$

Solve for x

$$x=7\sqrt{2}\approx 9.899494937$$

$$x=-7\sqrt{2}\approx -9.899494937$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -7,7 since division by zero is not defined. Multiply both sides of the equation by \left(x-7\right)\left(x+7\right).

$$7^{2}=\left(x-7\right)\left(x+7\right)$$

Calculate 7 to the power of 2 and get 49.

$$49=\left(x-7\right)\left(x+7\right)$$

Consider \left(x-7\right)\left(x+7\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 7.

$$49=x^{2}-49$$

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

$$x^{2}-49=49$$

Add 49 to both sides.

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

Add 49 and 49 to get 98.

$$x^{2}=98$$

Take the square root of both sides of the equation.

$$x=7\sqrt{2} x=-7\sqrt{2}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -7,7 since division by zero is not defined. Multiply both sides of the equation by \left(x-7\right)\left(x+7\right).

$$7^{2}=\left(x-7\right)\left(x+7\right)$$

Calculate 7 to the power of 2 and get 49.

$$49=\left(x-7\right)\left(x+7\right)$$

Consider \left(x-7\right)\left(x+7\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 7.

$$49=x^{2}-49$$

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

$$x^{2}-49=49$$

Subtract 49 from both sides.

$$x^{2}-49-49=0$$

Subtract 49 from -49 to get -98.

$$x^{2}-98=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -98 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-98\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-98\right)}}{2}$$

Multiply -4 times -98.

$$x=\frac{0±\sqrt{392}}{2}$$

Take the square root of 392.

$$x=\frac{0±14\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±14\sqrt{2}}{2} when ± is plus.

$$x=7\sqrt{2}$$

Now solve the equation x=\frac{0±14\sqrt{2}}{2} when ± is minus.

$$x=-7\sqrt{2}$$

The equation is now solved.

$$x=7\sqrt{2} x=-7\sqrt{2}$$