Solve -1/2=27+3-a^2/2-3*3

$$- \frac { 1 } { 2 } = \frac { 27 + 3 - a ^ { 2 } } { 2 - 3 \cdot 3 }$$

Solve for a

$$a = \frac{\sqrt{106}}{2} \approx 5.14781507$$

$$a = -\frac{\sqrt{106}}{2} \approx -5.14781507$$

Steps by Finding Square Root

Add 27 and 3 to get 30.

$$-\frac{1}{2}=\frac{30-a^{2}}{2-3\times 3}$$

Multiply 3 and 3 to get 9.

$$-\frac{1}{2}=\frac{30-a^{2}}{2-9}$$

Subtract 9 from 2 to get -7.

$$-\frac{1}{2}=\frac{30-a^{2}}{-7}$$

Multiply both numerator and denominator by -1.

$$-\frac{1}{2}=\frac{-30+a^{2}}{7}$$

Divide each term of -30+a^{2} by 7 to get -\frac{30}{7}+\frac{1}{7}a^{2}.

$$-\frac{1}{2}=-\frac{30}{7}+\frac{1}{7}a^{2}$$

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

$$-\frac{30}{7}+\frac{1}{7}a^{2}=-\frac{1}{2}$$

Add \frac{30}{7} to both sides.

$$\frac{1}{7}a^{2}=-\frac{1}{2}+\frac{30}{7}$$

Add -\frac{1}{2} and \frac{30}{7} to get \frac{53}{14}.

$$\frac{1}{7}a^{2}=\frac{53}{14}$$

Multiply both sides by 7, the reciprocal of \frac{1}{7}.

$$a^{2}=\frac{53}{14}\times 7$$

Multiply \frac{53}{14} and 7 to get \frac{53}{2}.

$$a^{2}=\frac{53}{2}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{106}}{2} a=-\frac{\sqrt{106}}{2}$$

Steps Using the Quadratic Formula

Add 27 and 3 to get 30.

$$-\frac{1}{2}=\frac{30-a^{2}}{2-3\times 3}$$

Multiply 3 and 3 to get 9.

$$-\frac{1}{2}=\frac{30-a^{2}}{2-9}$$

Subtract 9 from 2 to get -7.

$$-\frac{1}{2}=\frac{30-a^{2}}{-7}$$

Multiply both numerator and denominator by -1.

$$-\frac{1}{2}=\frac{-30+a^{2}}{7}$$

Divide each term of -30+a^{2} by 7 to get -\frac{30}{7}+\frac{1}{7}a^{2}.

$$-\frac{1}{2}=-\frac{30}{7}+\frac{1}{7}a^{2}$$

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

$$-\frac{30}{7}+\frac{1}{7}a^{2}=-\frac{1}{2}$$

Add \frac{1}{2} to both sides.

$$-\frac{30}{7}+\frac{1}{7}a^{2}+\frac{1}{2}=0$$

Add -\frac{30}{7} and \frac{1}{2} to get -\frac{53}{14}.

$$-\frac{53}{14}+\frac{1}{7}a^{2}=0$$

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.

$$\frac{1}{7}a^{2}-\frac{53}{14}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{7} for a, 0 for b, and -\frac{53}{14} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times \frac{1}{7}\left(-\frac{53}{14}\right)}}{2\times \frac{1}{7}}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times \frac{1}{7}\left(-\frac{53}{14}\right)}}{2\times \frac{1}{7}}$$

Multiply -4 times \frac{1}{7}.

$$a=\frac{0±\sqrt{-\frac{4}{7}\left(-\frac{53}{14}\right)}}{2\times \frac{1}{7}}$$

Multiply -\frac{4}{7} times -\frac{53}{14} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$a=\frac{0±\sqrt{\frac{106}{49}}}{2\times \frac{1}{7}}$$

Take the square root of \frac{106}{49}.

$$a=\frac{0±\frac{\sqrt{106}}{7}}{2\times \frac{1}{7}}$$

Multiply 2 times \frac{1}{7}.

$$a=\frac{0±\frac{\sqrt{106}}{7}}{\frac{2}{7}}$$

Now solve the equation a=\frac{0±\frac{\sqrt{106}}{7}}{\frac{2}{7}} when ± is plus.

$$a=\frac{\sqrt{106}}{2}$$

Now solve the equation a=\frac{0±\frac{\sqrt{106}}{7}}{\frac{2}{7}} when ± is minus.

$$a=-\frac{\sqrt{106}}{2}$$

The equation is now solved.

$$a=\frac{\sqrt{106}}{2} a=-\frac{\sqrt{106}}{2}$$