Question

Solve the quadratic by factoring.5x2 – 10 = 2x – 7

Answer 1

Given the followin Quadratic equation:

$5x^2-10=2x-7$

You need to follow these steps in order to solve it by factoring:

1- Subtract 2x from both sides of the equation:

$\begin{gathered} 5x^2-10-(2x)=2x-7-(2x) \\ 5x^2-10-2x=-7 \end{gathered}$

2. Add 7 to both sides of the equation:

$\begin{gathered} 5x^2-10-2x+(7)=-7+(7) \\ 5x^2-2x-3=0 \end{gathered}$

Now the equation has this form:

$ax^2+bx+c=0$

3. You can notice that the leading coefficient is:

$a=5$

Then, multiply and divide the trinomial by 5:

$\begin{gathered} \frac{5(5x^2-2x-3)}{5}=0 \\ \\ \frac{(5x)^2-2(5x)-3(5)}{5}=0 \\ \\ \frac{(5x)^2-2(5x)-15}{5}=0 \end{gathered}$

4. Now let's factor it:

Find two numbers whose sum is -2 and whose product is -15. These would be 3 and -5. Then:

$\frac{(5x-5)(5x+3)}{5}=0$

5. Simplify and find the solutions:

$\begin{gathered} \frac{(5x-5)(5x+3)}{5}=0 \\ \\ (x-1)(5x+3)=0 \\ \\ x_1=1 \\ \\ x_2=-\frac{3}{5} \end{gathered}$

The answer is:

$\begin{gathered} x_1=1 \\ x_2=-\frac{3}{5} \end{gathered}$