Question

solve for m. write answers in simplified form with fractions.
25m² + 11 = 13
show your work here
hint: to add the square root symbol (√□), type
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Explanation:

Step1: Isolate the squared term

Subtract 11 from both sides of the equation \(25m^{2}+11 = 13\).
\(25m^{2}=13 - 11\)
\(25m^{2}=2\)

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

Divide both sides by 25.
\(m^{2}=\frac{2}{25}\)

Step3: Solve for \(m\)

Take the square root of both sides. Remember that when taking the square root of a positive number, we get two solutions: positive and negative.
\(m=\pm\sqrt{\frac{2}{25}}\)
Simplify the square root. Since \(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\) (for \(a\geq0,b > 0\)), we have:
\(m=\pm\frac{\sqrt{2}}{\sqrt{25}}\)
And \(\sqrt{25} = 5\), so:
\(m=\pm\frac{\sqrt{2}}{5}\)

Answer:

\(m=\frac{\sqrt{2}}{5}\) or \(m =-\frac{\sqrt{2}}{5}\)