Solve (x-2):4=7:(x+2)

$$( x - 2 ) : 4 = 7 : ( x + 2 )$$

Solve for x

$$x=4\sqrt{2}\approx 5.656854249$$

$$x=-4\sqrt{2}\approx -5.656854249$$

Steps by Finding Square Root

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 4\left(x+2\right), the least common multiple of 4,x+2.

$$\left(x+2\right)\left(x-2\right)=4\times 7$$

Consider \left(x+2\right)\left(x-2\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 2.

$$x^{2}-4=4\times 7$$

Multiply 4 and 7 to get 28.

$$x^{2}-4=28$$

Add 4 to both sides.

$$x^{2}=28+4$$

Add 28 and 4 to get 32.

$$x^{2}=32$$

Take the square root of both sides of the equation.

$$x=4\sqrt{2} x=-4\sqrt{2}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 4\left(x+2\right), the least common multiple of 4,x+2.

$$\left(x+2\right)\left(x-2\right)=4\times 7$$

Consider \left(x+2\right)\left(x-2\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 2.

$$x^{2}-4=4\times 7$$

Multiply 4 and 7 to get 28.

$$x^{2}-4=28$$

Subtract 28 from both sides.

$$x^{2}-4-28=0$$

Subtract 28 from -4 to get -32.

$$x^{2}-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-32\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-32\right)}}{2}$$

Multiply -4 times -32.

$$x=\frac{0±\sqrt{128}}{2}$$

Take the square root of 128.

$$x=\frac{0±8\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{2}}{2} when ± is plus.

$$x=4\sqrt{2}$$

Now solve the equation x=\frac{0±8\sqrt{2}}{2} when ± is minus.

$$x=-4\sqrt{2}$$

The equation is now solved.

$$x=4\sqrt{2} x=-4\sqrt{2}$$