Question

Solve the equation by factoring. 5x^2+7x-66=0X= _____ Simplify your answer.

Answer 1

`x=3,-4(2)/(5)`

Explanation:

Given the quadratic equation:

`5x^2+7x-66=0`

We want to solve for x by factoring.

To factorize, follow the steps below.

Step 1: Multiply the coefficient of x² and the constant.

`5*-66`

Step 2: Find two numbers that multiply to give (5 x -66), and add to give the coefficient of x, 7.

`\begin{gathered} 5*-3*22=-15*22 \\ 22-15=7 \end{gathered}`

Step 3: Rewrite the middle term with those numbers.

`\begin{gathered} 5x^2+7x-66=0 \\ 5x^2+22x-15x-66=0 \end{gathered}`

Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.

`\begin{gathered} x(5x+22)-3(5x+22)=0 \\ (x-3)(5x+22)=0 \end{gathered}`

Step 5: Solve for x

`\begin{gathered} x-3=0\text{ or }5x+22=0 \\ x=3\text{ or 5x=-22} \\ x=3\text{ or }x=-(22)/(5) \\ x=3\text{ or }x=-4(2)/(5) \end{gathered}`

The value of x is 3 or -4 2/5.