Question

Solve the equation (x-4) (x+9) = 0
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Answer 1

x = 4,-9

Explanation:

This is a quadratic equation in x-intercept pattern. Since this is completely factored, we can simply solve the equation like a linear.

First, separate two equations. Let r be the roots of equation, therefore:

`\displaystyle \large{r=\begin{cases}x-4=0\\ x+9=0 \end{cases}}`

I use the r-variable to denote the roots of equations (not necessary), simply separate both then solve it like a linear.

`\displaystyle \large{r=\begin{cases}x-4+4=0+4\\ x+9-9=0-9 \end{cases}}\\\displaystyle \large{r=\begin{cases}x=4\\ x=-9 \end{cases}}`

Therefore, the roots of equation are x = 4 or x = -9. In short, we can write as x = 4,-9.

The reason why we use OR instead of AND because one of x-values satisfy the quadratic equation hence ‘or’ is more suitable than ‘and’. However, you must write all valid solutions instead of writing only one x-value from two.

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Let me know in the comment if you have any questions.