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

1 Answer
smendyka
Jul 2, 2017

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

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