Answer:
[tex]x=3,-4\frac{2}{5}[/tex]Explanation:
Given the quadratic equation:
[tex]5x^2+7x-66=0[/tex]We want to solve for x by factoring.
To factorize, follow the steps below.
Step 1: Multiply the coefficient of x² and the constant.
[tex]5\times-66[/tex]Step 2: Find two numbers that multiply to give (5 x -66), and add to give the coefficient of x, 7.
[tex]\begin{gathered} 5\times-3\times22=-15\times22 \\ 22-15=7 \end{gathered}[/tex]Step 3: Rewrite the middle term with those numbers.
[tex]\begin{gathered} 5x^2+7x-66=0 \\ 5x^2+22x-15x-66=0 \end{gathered}[/tex]Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.
[tex]\begin{gathered} x(5x+22)-3(5x+22)=0 \\ (x-3)(5x+22)=0 \end{gathered}[/tex]Step 5: Solve for x
[tex]\begin{gathered} x-3=0\text{ or }5x+22=0 \\ x=3\text{ or 5x=-22} \\ x=3\text{ or }x=-\frac{22}{5} \\ x=3\text{ or }x=-4\frac{2}{5} \end{gathered}[/tex]The value of x is 3 or -4 2/5.