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Solve the equation x^2 - 18x + 46 = 3x

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wondergirl | Student, Grade 10 | eNoter

Posted April 15, 2013 at 5:00 AM via web

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Solve the equation x^2 - 18x + 46 = 3x

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 15, 2013 at 5:03 AM (Answer #1)

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The equation x^2 - 18x + 46 = 3x has to be solved for x.

x^2 - 18x + 46 = 3x

=> x^2 - 18x + 46 - 3x = 0

=> x^2 - 21x + 46 = 0

x1 = `(21 + sqrt(21^2 - 4*46))/2 = (21 + sqrt 257)/2`

x2 = `(21 - sqrt 257)/2`

The solution of the equation x^2 - 18x + 46 = 3x is `(21 + sqrt 257)/2` and `(21 - sqrt 257)/2`

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rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted April 15, 2013 at 5:32 AM (Answer #2)

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Given quadratic equation is `x^2-18x+46=3x`

                            or,      `x^2-21x+46=0` .

Let `x=a` and `x=b`  be the two roots of the given equation. So we can write

                `x^2-21x+46=(x-a)(x-b)`

or,           `x^2-21x+46=x^2-(a+b)x+ab`

Comparing various powers of `x`  we get

         `(a+b)=21`     (1)    and    `ab=46`           (2).

We know that    `(a-b)^2=(a+b)^2-4ab`

So,     `(a-b)^2=21^2-4.46=257`

or,      `(a-b)=+-sqrt257` ..............(3)

Using equation (1) and (3) we get (by considering positive sign for (a-b))

             `2a=21+sqrt257`

or,           `a=(21+sqrt257)/2`

and        `b=(21-sqrt257)/2` .

If we take -sign for the value of (a-b) we get

          `a=(21-sqrt257)/2`

and     `b=(21+sqrt257)/2` .

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oldnick | Valedictorian

Posted April 15, 2013 at 3:34 PM (Answer #3)

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`x^2-18x +46=3x`

subrtacting `3x` both sides:


`x^2-18x+46-3x=3x-3x`

`x^2-21x+46=0`

re-wrting:

`x^2- 2x(21/2) +441/4 - 257/4=0`

`(x-21/2)^2=257/4`

extracting square root both sides:

`x-21/2= +-1/2sqrt(257)`

so:  `x=(21+-sqrt(257))/2`

`x_1=18,5156`    `x_2= 2,4844`

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