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3 years ago

15

How do you solve radical 2x plus 5 equals x?

2 answers:

Ksenya-84 [330]3 years ago

8 0

X=-5 is your answer. Hope this helps :)

Brums [2.3K]3 years ago

8 0

Radical 2x+5 equals x

1. Square both side.

2x+5 equals x square

Move everything to one side.
X square-2x-5=0

Since this time, we can't factor very well. We need to use the quadratic formula.

-b+- square root b square- 4ac divided by 2a

This gives: -(-2)* square root( 4-4(1)(5))/ 2

Notice that we get 2 plus and minus square root of -16.

Which is an imagery/ complex solution.

The value of x could be 2+i4/2 or 2-i4/2

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3 years ago

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3 years ago

Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,3) E (8,3) and F(1,-5).

NemiM [27]

Let the coordinates of the circumcentre O of the triangle DEF be (x, y). Circumcentre of a triangle is equidistant from each of the vertices.

1. Distance OD=distance OE, then:

$(x-1)^2+(y-3)^2=(x-8)^2+(y-3)^2$ .

2. Distance OD=distance OE, then:

$(x-1)^2+(y-3)^2=(x-1)^2+(y+5)^2$ .

Solve the system:

$\left\{\begin{array}{l} (x-1)^2+(y-3)^2=(x-8)^2+(y-3)^2 \\ (x-1)^2+(y-3)^2=(x-1)^2+(y+5)^2 \end{array}\right.$ ,

$\left\{\begin{array}{l} x^2-2x+1+y^2-6y+9=x^2-16x+64+y^2-6y+9 \\ x^2-2x+1+y^2-6y+9=x^2-2x+1+y^2+10y+25 \end{array}\right.$ ,

$\left\{\begin{array}{l} 14x=63 \\ -16y=16 \end{array}\right.$ .

Then

$x=\dfrac{63}{14} =\dfrac{9}{2} =4.5,\\ \\ y=-1$ .

Answer: the coordinates of the circumcenter for ∆DEF are x=4.5, y=-1.

5 0

4 years ago