The rectangular has an area of 5400 cm^2. What is the value of w?
5400 = (w)(2w - 30)
5400 = 2w^2 - 30 w
5400 = 2w(w - 15)
Now I am stuck. My choices are:
-45 cm
45 cm
60 cm
90 cm
What do I need to do next to get the correct answer? Thanks.
the answer is 60 if you were wondering
To solve the equation 5400 = 2w(w - 15), you can start by simplifying it further:
Divide both sides by 2:
2700 = w(w - 15)
Rearrange the equation:
w^2 - 15w - 2700 = 0
At this point, you have a quadratic equation in terms of w. You can use various methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula.
Since factoring is not apparent in this case, you can use the quadratic formula:
w = (-b ± √(b^2 - 4ac)) / 2a
In this equation, the quadratic equation is in the form ax^2 + bx + c = 0. For our equation w^2 - 15w - 2700 = 0, the values of a, b, and c can be identified as follows:
a = 1
b = -15
c = -2700
Now, substitute these values into the quadratic formula:
w = (-(-15) ± √((-15)^2 - 4(1)(-2700))) / (2(1))
Simplifying further:
w = (15 ± √(225 + 10800)) / 2
This gives you two possible solutions for w:
w = (15 ± √11025) / 2
Now, calculate the values inside the square root:
√11025 = 105
Substituting this back into the equation:
w = (15 ± 105) / 2
This gives you two possibilities for w:
w1 = (15 + 105) / 2 = 120 / 2 = 60
w2 = (15 - 105) / 2 = -90 / 2 = -45 (which is extraneous in this context)
Therefore, the value of w is 60 cm.
Don't factor in 3.
Instead, divide equation 2 by 2.
Set the equation equal to zero.
Factor the expression (......)(......) = 0
If it won't factor, complete the square or use the quadratic formula.