The area of a rectangular playing field is 192square meters. The length of the field is x+12 and the width is x-4. How do you calculate x by using quadratic formula?

Answer 1

#x = 12#

As far as we are aware, a rectangle's area formula is:

#"length" color(white)"." xx color(white)"." "width" color(white)"." = color(white)"." "area"#

Thus, by entering these values, we can express everything in terms of a quadratic, which the quadratic formula allows us to solve.

#(x+12) xx (x-4) = 192#

Let's enlarge the left side using the FOIL method.

#underbrace((x)(x)) _ "First" + underbrace((x)(-4)) _ "Outer" + underbrace((12)(x)) _ "Inner" + underbrace((12)(-4))_"Last" = 192#
#x^2 + (-4x) + (12x) + (-48) = 192#
#x^2 + 8x - 48 = 192#
Now subtract #192# from both sides.
#x^2 + 8x - 240 = 0#

Since this is a quadratic, we can solve it using the quadratic formula.

#a = 1# #b = 8# #c = -240#
#x = (-b+-sqrt(b^2-4ac))/(2a)#

Now enter all of those values and make things simpler.

#x = (-(8)+-sqrt((8)^2-4(1)(-240)))/(2(1))#
#x = (-8+-sqrt(64+960))/2#
#x = (-8+-sqrt1024)/2#
Note that #1024 = 2^10 = (2^5)^2 = 32^2#
#x = (-8+-sqrt(32^2))/2#
#x = (-8+-32)/2#
#x = -4+-16#
This means our two values of #x# are:
#x = -4-16 " " and " " x = -4+16#
#x = -20 " " and " " x = 12#
Remember that #x# represents a length, and so it cannot possibly be negative. This leaves us with only one solution:
#x = 12#

Last Response

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To calculate the value of ( x ) using the quadratic formula, you need to set up an equation based on the given information.

The area of a rectangle is given by the formula: [ \text{Area} = \text{Length} \times \text{Width} ]

Given: [ \text{Area} = 192 , \text{m}^2 ] [ \text{Length} = x + 12 ] [ \text{Width} = x - 4 ]

So, the equation becomes: [ 192 = (x + 12)(x - 4) ]

Expanding the equation: [ 192 = x^2 + 12x - 4x - 48 ]

Combining like terms: [ 192 = x^2 + 8x - 48 ]

Rearranging terms to form a quadratic equation in standard form: [ x^2 + 8x - 192 = 0 ]

Now, you can apply the quadratic formula: [ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} ]

Where: [ a = 1 ] [ b = 8 ] [ c = -192 ]

Substitute these values into the quadratic formula and solve for ( x ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7