Q40. - Algebra 1

Question

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.

$d^2-5d+6=0$

Step-by-Step Solution

Answer

The solutions of the quadratic equations are 3 and 2. 

Step 1. Understand the concept used .

If $a{x}^2+bx+c=0$, with $a\ne 0$, then $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$. Solving using factoring can be done by splitting the middle term of the equation and then making groups and equating them to zero.

Step 2. Substitute the values .

It is given that $d^2-5d+6=0$. Using the quadratic formula $d=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 1 for $a, -5$ for $b$ and 6 for $c$.

Put the values in the formula and get $d=\frac{-\left(-5\right)\pm \sqrt{{\left(-5\right)}^2-4\times \left(1\right)\times \left(6\right)}}{2\left(1\right)}$. 

Step 3. Write the solutions.

Simplify the expression for $d$.

$d=\frac{-\left(-5\right)\pm \sqrt{{\left(-5\right)}^2-4\times \left(1\right)\times \left(6\right)}}{2\left(1\right)}$

   $$\begin{gathered} =\frac{5\pm \sqrt{25-24}}{2} \\ =\frac{5\pm \sqrt{1}}{2} \\ =\frac{5\pm 1}{2} \end{gathered}$$

Therefore, either

 $$\begin{gathered} d=\frac{5+1}{2} \\ =3 \end{gathered}$$

or,

$$\begin{gathered} d=\frac{5-1}{2} \\ =2 \end{gathered}$$

that is., either $d=3$ or $d=2$.