Find the value of x.
The area of a rectangle = 105
The length is 2x+1
Width is x
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I tried solving it :
Arec = l x w
105 = (2x+1)x
105 = 2x^2 + x
0= 2x^2 + x - 105
This is where I get stuck on...
quadratic equation
x = [ -1 +/- sqrt (1+840)]/4
= [ -1 +/- 29 ]/4
= 28/4 forget negative solution
= 7
or
(x - 7) (2x + 15) = 0
To find the value of x, you can solve the quadratic equation 2x^2 + x - 105 = 0 by factoring, completing the square, or by using the quadratic formula.
Let's solve it by factoring:
0 = 2x^2 + x - 105
First, let's factor out the common factor of 2:
0 = 2(x^2 + 0.5x - 52.5)
Now, let's factor the quadratic expression inside the parentheses:
0 = 2(x + 10)(x - 5.25)
To find the value of x, set each factor equal to zero and solve for x:
x + 10 = 0 or x - 5.25 = 0
Solving for x in each equation:
x = -10 or x = 5.25
So, the possible values for x are -10 and 5.25.
To find the value of x, we can solve the quadratic equation that you have obtained: 0 = 2x^2 + x - 105.
One way to solve this quadratic equation is by factoring. However, in this case, factoring may be a bit challenging because the coefficient of x^2 is 2.
An alternative method is to use the quadratic formula, which states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 2, b = 1, and c = -105. Plugging these values into the quadratic formula, we get:
x = (-1 ± √(1^2 - 4(2)(-105))) / (2(2))
Simplifying further:
x = (-1 ± √(1 + 840)) / 4
x = (-1 ± √841) / 4
x = (-1 ± 29) / 4
Evaluating both solutions:
x1 = (-1 + 29) / 4 = 28/4 = 7
x2 = (-1 - 29) / 4 = -30/4 = -7.5
Therefore, the value of x can be either 7 or -7.5.