If a ractangle has a length of 2x-1 and width x+5 and has an area of 156 square units, what is x?
(2x-1)(x+5) = 156
That can be rewritten as
2x^2 + 9x - 5 = 156
2x^2 + 9x - 161 = 0
(2x + 23)(x - 7) = 0
Either x = 7 or -23/2 will work.
The answer has to be positive, so it has to be x = 7.
Thanks
To find the value of x, we first need to set up an equation based on the information given.
The formula for the area of a rectangle is A = length * width. In this case, the area of the rectangle is given as 156 square units, and the length and width are expressed in terms of x.
So, we can write the equation as:
(2x - 1) * (x + 5) = 156
To solve this equation, we can expand the expression:
2x^2 + 9x - x - 5 = 156
Combining like terms:
2x^2 + 8x - 5 = 156
Rearranging and subtracting 156 from both sides:
2x^2 + 8x - 161 = 0
Now, we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula.
In this case, the equation cannot be easily factored or simplified, so we will use the quadratic formula:
The quadratic formula states that for an equation ax^2 + bx + c = 0, the value of x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation 2x^2 + 8x - 161 = 0, a = 2, b = 8, and c = -161.
Plugging these values into the quadratic formula:
x = (-8 ± √(8^2 - 4 * 2 * -161)) / (2 * 2)
Simplifying:
x = (-8 ± √(64 + 1288)) / 4
x = (-8 ± √1352) / 4
x ≈ (-8 ± 36.77) / 4
Now we have two possible solutions for x:
x ≈ (-8 + 36.77) / 4 ≈ 7.94
x ≈ (-8 - 36.77) / 4 ≈ -11.44
Since the sides of a rectangle cannot be negative, we can discard the negative value.
Therefore, x ≈ 7.94
So, the value of x is approximately 7.94 units.