The area of a rectangle is given by A = x2 + 4x – 5. Find the value of x if the total area of the rectangle is equal to 7 square units.
Yes
To find the value of x, we need to set up an equation using the given information.
The area of a rectangle is given by the formula A = length × width. In this case, the length and width are represented by the variable x.
We are given that the area of the rectangle is equal to 7 square units, so we can set up the equation:
x^2 + 4x - 5 = 7
To solve this equation, we need to isolate the variable x.
First, we can move the constant term (7) to the other side of the equation by subtracting 7 from both sides:
x^2 + 4x - 5 - 7 = 0
Simplifying further:
x^2 + 4x - 12 = 0
Now, we need to solve this quadratic equation. There are different methods to solve it, such as factoring, using the quadratic formula, or completing the square. In this case, let's try factoring:
(x - 2)(x + 6) = 0
Now, we have two factors: (x - 2) and (x + 6). To find the value of x, we can set each factor equal to zero and solve for x:
x - 2 = 0 or x + 6 = 0
Solving these equations:
x = 2 or x = -6
Therefore, the value of x can be either 2 or -6.
7 = x^2 + 4 x -5
x^2 + 4 x - 12 = 0
(x+6)(x-2) = 0
x = 2 (negative 6 not useful)