Question

homework 9: section 2.5
score: 25/280 answered: 2/28
question 3
solve.
25x² - 64 = 0
x =
question help: video message instructor

Explanation:

Step1: Isolate the squared term

We start with the equation \(25x^{2}-64 = 0\). First, we add 64 to both sides of the equation to isolate the \(x^{2}\) term.
\(25x^{2}-64 + 64=0 + 64\)
\(25x^{2}=64\)

Step2: Solve for \(x^{2}\)

Next, we divide both sides of the equation by 25 to solve for \(x^{2}\).
\(x^{2}=\frac{64}{25}\)

Step3: Take the square root of both sides

To solve for \(x\), we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution.
\(x=\pm\sqrt{\frac{64}{25}}\)

Step4: Simplify the square root

We know that \(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\) (for \(a\geq0\) and \(b > 0\)). So we can simplify \(\sqrt{\frac{64}{25}}\) as \(\frac{\sqrt{64}}{\sqrt{25}}\). Since \(\sqrt{64} = 8\) and \(\sqrt{25}=5\), we have:
\(x=\pm\frac{8}{5}\)

Answer:

\(x=\frac{8}{5}\) or \(x =-\frac{8}{5}\) (or in boxed form, if we consider each solution separately, \(\boxed{\frac{8}{5}}\) and \(\boxed{-\frac{8}{5}}\); but since the problem might expect both solutions together, we can write \(x=\pm\frac{8}{5}\))