Question

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$a^{2}+3=12$$

Short answer

The solutions to the equation \(a^{2}+3=12\) are \(a=3\) and \(a=-3\).

Step-by-step solution

Identify the equation

The given equation is \(a^{2}+3=12\).

Isolate the variable term

To isolate the variable term, subtract 3 from both sides of the equation, giving an equation of the form \(a^{2}=12-3\).

Simplify the equation

Simplify the right side of the equation to \(a^{2}=9\).

Solve for 'a'

The solutions will be obtained by taking the square root of both sides. This gives us \(a=\sqrt{9}\) and \(a=-\sqrt{9}\).

Simplify the result

Finally, simplify to find the solutions \(a=3\) and \(a=-3\).