Question

question
use the quadratic formula to solve. express your answer in simplest form.
25k² + 36k + 9 = 6k
answer attempt 1 out of 2
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Explanation:

Step1: Rearrange the equation to standard quadratic form \(ax^2 + bx + c = 0\)

Given equation: \(25k^2 + 36k + 9 = 6k\)
Subtract \(6k\) from both sides: \(25k^2 + 36k - 6k + 9 = 0\)
Simplify: \(25k^2 + 30k + 9 = 0\)
Here, \(a = 25\), \(b = 30\), \(c = 9\)

Step2: Apply the quadratic formula \(k=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)

First, calculate the discriminant \(D = b^2 - 4ac\)
Substitute \(a = 25\), \(b = 30\), \(c = 9\):
\(D=(30)^2 - 4\times25\times9\)
\(= 900 - 900\)
\(= 0\)

Now, substitute \(a = 25\), \(b = 30\), \(D = 0\) into the quadratic formula:
\(k=\frac{-30\pm\sqrt{0}}{2\times25}\)
\(=\frac{-30\pm0}{50}\)

Step3: Simplify the expression

Since \(\pm0\) doesn't change the value, we have:
\(k=\frac{-30}{50}\)
Simplify the fraction by dividing numerator and denominator by 10:
\(k = -\frac{3}{5}\)

Answer:

\(k = -\dfrac{3}{5}\)