Skill 3 of 12

Solve quadratic equations using square roots

Solve equations of the form $ax^2+c=0$ and $a(x-h)^2=k$ with real solutions by isolating the square and taking square roots.

Common Core standards: A-REI.4b
Builds on: Nothing earlier in this unit. This is where it starts.

Common mistakes

What students most often get wrong with this skill:

Forgetting the negative square root (plus-or-minus)
Taking the square root before isolating the squared term
Not simplifying the radical in the answer

A worked example

From the lesson, with every step explained.

Example 1: square already alone

Problem. Solve $x^2=49$ .

Plan. The square is already alone, so we can take the square root right away.

1) Take the square root of both sides. We use $\pm$ because both a positive and a negative number square to 49.

x=\pm\sqrt{49}

2) Simplify, since $\sqrt{49}=7$ .

x=\pm 7

Answer. $x=7$ or $x=-7$ .

Check.

$7^2=49$

$(-7)^2=49$

Both work. The graph of $y=x^2-49$ crosses the x-axis at $-7$ and $7$ .

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