Question

solve for d.
5d^{2}-9d - 2 = 0
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
d =

Explanation:

Step1: Factor the quadratic equation

We need to factor \(5d^{2}-9d - 2=0\). We look for two numbers that multiply to \(5\times(- 2)=-10\) and add up to \(-9\). The numbers are \(-10\) and \(1\). So we can rewrite the middle - term: \(5d^{2}-10d + d-2 = 0\). Then factor by grouping: \(5d(d - 2)+1(d - 2)=0\), which gives \((5d + 1)(d - 2)=0\).

Step2: Set each factor equal to zero

If \(5d+1 = 0\), then \(5d=-1\), and \(d=-\frac{1}{5}\). If \(d - 2=0\), then \(d = 2\).

Answer:

\(d = 2,-\frac{1}{5}\)