Solve |-1|-1/2*6a^2=7

$$| - 1 | - \frac { 1 } { 2 } \times 6 a ^ { 2 } = 7$$

Solve for a

$$a=-\sqrt{2}i\approx -0-1.414213562i$$

$$a=\sqrt{2}i\approx 1.414213562i$$

Steps by Finding Square Root

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of -1 is 1.

$$1-\frac{1}{2}\times 6a^{2}=7$$

Multiply \frac{1}{2} and 6 to get 3.

$$1-3a^{2}=7$$

Subtract 1 from both sides.

$$-3a^{2}=7-1$$

Subtract 1 from 7 to get 6.

$$-3a^{2}=6$$

Divide both sides by -3.

$$a^{2}=\frac{6}{-3}$$

Divide 6 by -3 to get -2.

$$a^{2}=-2$$

The equation is now solved.

$$a=\sqrt{2}i a=-\sqrt{2}i$$

Steps Using the Quadratic Formula

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of -1 is 1.

$$1-\frac{1}{2}\times 6a^{2}=7$$

Multiply \frac{1}{2} and 6 to get 3.

$$1-3a^{2}=7$$

Subtract 7 from both sides.

$$1-3a^{2}-7=0$$

Subtract 7 from 1 to get -6.

$$-6-3a^{2}=0$$

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.

$$-3a^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-3\right)\left(-6\right)}}{2\left(-3\right)}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-3\right)\left(-6\right)}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$a=\frac{0±\sqrt{12\left(-6\right)}}{2\left(-3\right)}$$

Multiply 12 times -6.

$$a=\frac{0±\sqrt{-72}}{2\left(-3\right)}$$

Take the square root of -72.

$$a=\frac{0±6\sqrt{2}i}{2\left(-3\right)}$$

Multiply 2 times -3.

$$a=\frac{0±6\sqrt{2}i}{-6}$$

Now solve the equation a=\frac{0±6\sqrt{2}i}{-6} when ± is plus.

$$a=-\sqrt{2}i$$

Now solve the equation a=\frac{0±6\sqrt{2}i}{-6} when ± is minus.

$$a=\sqrt{2}i$$

The equation is now solved.

$$a=-\sqrt{2}i a=\sqrt{2}i$$