Question

solving quadratics with square roots (lev
question
examples
solve the following quadratic equation
for all values of ( x ) in simplest form.
( 2(x^2 - 9) + 1 = 1 )
answer
attempt 1 out of 2
additional solution no solution
( x = )
submit answer
( pm ) ( sqrt{quad} )

Explanation:

Step1: Simplify the equation

First, we start with the given equation \(2(x^{2}-9)+1 = 1\). Subtract 1 from both sides of the equation:
\(2(x^{2}-9)+1 - 1=1 - 1\)
\(2(x^{2}-9)=0\)

Step2: Divide both sides by 2

Divide each side of the equation \(2(x^{2}-9)=0\) by 2:
\(\frac{2(x^{2}-9)}{2}=\frac{0}{2}\)
\(x^{2}-9 = 0\)

Step3: Solve for \(x^{2}\)

Add 9 to both sides of the equation \(x^{2}-9 = 0\):
\(x^{2}-9 + 9=0 + 9\)
\(x^{2}=9\)

Step4: Take square roots

Take the square root of both sides. Remember that if \(x^{2}=a\) (\(a\geq0\)), then \(x=\pm\sqrt{a}\). So for \(x^{2}=9\), we have:
\(x=\pm\sqrt{9}\)
Since \(\sqrt{9} = 3\), we get \(x=\pm3\)

Answer:

\(\pm 3\)