Q. 6.90 - Intermediate Algebra

Question

Solve, $2d^2-5d=3$

Step-by-Step Solution

Answer

The value is $d=-\frac{1}{2},3$

Step 1: Given information

Given the equation $2d^2-5d=3$

Step 2: Writing in standard form

Writing in standard form, we get

$$\begin{gathered} 2d^2-5d=3 \\ 2d^2-5d-3=0 \\ 2d^2-6d+d-3=0 \\ 2d(d-3)+1(d-3)=0 \\ (2d+1)(d-3)=0 \\ d=-\frac{1}{2},3 \end{gathered}$$

Step 3: Checking the values

SUbstituting and checking the values, we get

$$\begin{gathered} 2{\left(\frac{-1}{2}\right)}^2-5\left(\frac{-1}{2}\right)=3 \\ \frac{1}{2}+\frac{5}{2}=3 \\ 3=3 \end{gathered}$$

Step 4: Checking the values

Substituting values and checking the value, we get

$$\begin{gathered} 2{\left(3\right)}^2-5\left(3\right)=3 \\ 18-15=3 \\ 3=3 \end{gathered}$$

This is true