If (x – 7)(x + 4) = 0, then x =
Understand the Problem
The question is asking to solve the equation (x – 7)(x + 4) = 0 for the value of x. We know that for a product of two factors to equal zero, at least one of the factors must equal zero. Therefore, we can set each factor equal to zero and solve for x.
Answer
The values of $x$ are $7$ and $-4$.
Answer for screen readers
The values of $x$ that satisfy the equation $(x - 7)(x + 4) = 0$ are $x = 7$ and $x = -4$.
Steps to Solve
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Set each factor to zero
To solve the equation $(x - 7)(x + 4) = 0$, we can set each factor equal to zero. -
Solve the first factor
For the first factor, set $x - 7 = 0$.
Add 7 to both sides:
$$ x - 7 + 7 = 0 + 7 $$
Thus,
$$ x = 7 $$ -
Solve the second factor
Now, for the second factor, set $x + 4 = 0$.
Subtract 4 from both sides:
$$ x + 4 - 4 = 0 - 4 $$
Hence,
$$ x = -4 $$ -
List the solutions
The solutions to the equation are $x = 7$ and $x = -4$.
We can summarize this as the final solutions of the equation.
The values of $x$ that satisfy the equation $(x - 7)(x + 4) = 0$ are $x = 7$ and $x = -4$.
More Information
The solutions to the equation reflect the x-intercepts of the parabola represented by the equation $y = (x - 7)(x + 4)$. At these points, the value of $y$ equals zero.
Tips
- Forgetting to set both factors equal to zero. Make sure to solve for both $x - 7 = 0$ and $x + 4 = 0$.
- Making calculation errors when isolating $x$. Take care during the arithmetic steps to avoid mistakes.
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