Solving $x^2 = a$
Master Solving $x^2 = a$ in Grade 9 Saxon Algebra 1. Property For equations like , solve by taking the square root of both sides (Saxon Algebra 1, Grade 9)
Key Concepts
Property For equations like $x^2 = a$, solve by taking the square root of both sides. This gives two solutions: $x = \pm\sqrt{a}$. Explanation Reversing a square usually gives two answers! Since both $5^2$ and $( 5)^2$ equal 25, the square root of 25 must be both 5 and 5. Don't forget the negative twin! Examples $x^2 = 36 \implies x = \pm\sqrt{36} \implies x = \pm 6$ $x^2 = 9 \implies$ No real solution exists.
Common Questions
How do you solve an equation of the form x² = a?
Take the square root of both sides and remember to include both the positive and negative roots. The solution is x = ±√a. Simplify the radical if possible, or leave it in exact form.
Why do equations of the form x² = a have two solutions?
Squaring a positive or negative number gives the same positive result, so both x = √a and x = -√a satisfy x² = a. Missing the negative root is the most common error when solving this type of equation.
What happens when a is negative in x² = a?
If a is negative, there is no real solution because no real number squared produces a negative result. You would write 'no real solution.' This connects to even roots of negative numbers being undefined in the real number system.