Solve (1.2+x)*(1.2-x)=108

$$( 1.2 + x ) \times ( 1.2 - x ) = 108$$

Solve for x (complex solution)

$$x=-\frac{i\times 6\sqrt{74}}{5}\approx -0-10.32279032i$$

$$x=\frac{i\times 6\sqrt{74}}{5}\approx 10.32279032i$$

Steps by Finding Square Root

Consider \left(1.2+x\right)\left(1.2-x\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 1.2.

$$1.44-x^{2}=108$$

Subtract 1.44 from both sides.

$$-x^{2}=108-1.44$$

Subtract 1.44 from 108 to get 106.56.

$$-x^{2}=106.56$$

Divide both sides by -1.

$$x^{2}=\frac{106.56}{-1}$$

Expand \frac{106.56}{-1} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{10656}{-100}$$

Reduce the fraction \frac{10656}{-100} to lowest terms by extracting and canceling out 4.

$$x^{2}=-\frac{2664}{25}$$

The equation is now solved.

$$x=\frac{6\sqrt{74}i}{5} x=-\frac{6\sqrt{74}i}{5}$$

Steps Using the Quadratic Formula

Consider \left(1.2+x\right)\left(1.2-x\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 1.2.

$$1.44-x^{2}=108$$

Subtract 108 from both sides.

$$1.44-x^{2}-108=0$$

Subtract 108 from 1.44 to get -106.56.

$$-106.56-x^{2}=0$$

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.

$$-x^{2}-\frac{2664}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -\frac{2664}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-\frac{2664}{25}\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-\frac{2664}{25}\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-\frac{2664}{25}\right)}}{2\left(-1\right)}$$

Multiply 4 times -\frac{2664}{25}.

$$x=\frac{0±\sqrt{-\frac{10656}{25}}}{2\left(-1\right)}$$

Take the square root of -\frac{10656}{25}.

$$x=\frac{0±\frac{12\sqrt{74}i}{5}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±\frac{12\sqrt{74}i}{5}}{-2}$$

Now solve the equation x=\frac{0±\frac{12\sqrt{74}i}{5}}{-2} when ± is plus.

$$x=-\frac{6\sqrt{74}i}{5}$$

Now solve the equation x=\frac{0±\frac{12\sqrt{74}i}{5}}{-2} when ± is minus.

$$x=\frac{6\sqrt{74}i}{5}$$

The equation is now solved.

$$x=-\frac{6\sqrt{74}i}{5} x=\frac{6\sqrt{74}i}{5}$$