How do you solve #a^2+3=51#?

1 Answer
Jul 2, 2017

Answer:

See a solution process below:

Explanation:

First, subtract #color(red)(3)# from each side of the equation to isolate the #a# term while keeping the equation balanced:

#a^2 + 3 - color(red)(3) = 51 - color(red)(3)#

#a^2 + 0 = 48#

#a^2 = 48#

Now, take the square root of each side of the equation to solve for #a# while keeping the equation balanced. Remember, the square root of a number produces a positive and negative result:

#sqrt(a^2) = +-sqrt(48)#

#a = +-sqrt(48)#

We can rewrite the radical and simplify using this rule for radicals:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#a = +-sqrt(16 * 3)#

#a = +-sqrt(16) * sqrt(3)#

#a = +-4sqrt(12)#

If necessary, the numerical answer is:

#a = +-6.928# rounded to the nearest thousandth