Solving of Quadratic Equations...?

Question

Can u please help me and explain how to solve incomplete quadratic equations and answer it by factoring... i give u some problem,

1. 10x^2 = 250

Answer 1

OK, we need to isolate the 'x' term. This is how we solve any equation. We do this by opposing any operation done to 'x', by performing the inverse operation to both sides of the equation. It's really quite simple =)

Like so...

10x^2 = 250

x^2 = 25          {dividing both sides by 10, to undo the coefficient of x}

squareroot(x^2) = squareroot(25)          {taking the square root of both sides to undo the exponent of x)

x = plus or minus 5.          {(-5)^2 and (5)^2 both = 25}

If you have any more troubles please don't hesitate to e-mail me =)

max

Answer 2

hi

10x^2-250=0

10(x^2-25)=0

x^2-25=0  ==>  (x-5)(x+5)=0

x=5  ,  x=-5

Answer 3

10x^2 = 250

x^2 =25

x=+- 25

Answer 4

10x^2 = 250

divide both sides by 10 we get

x^2=25

x=sqrt(25)   ---->answer

Answer 5

Question Number 1 :

For this equation 10*x^2  = 250 , answer the following questions :

A. Find the roots using Quadratic Formula !

B. Use factorization to find the root of the equation !

C. Use completing the square to find the root of the equation !

Answer Number 1 :

First, we have to turn equation : 10*x^2  = 250 , into a*x^2+b*x+c=0 form.

10*x^2  = 250 , move everything in the right hand side, to the left hand side of the equation

<=> 10*x^2  - ( 250 ) = 0 , which is the same with

<=> 10*x^2  + ( - 250 ) =0 , now open the bracket and we get

<=> 10*x^2 - 250 = 0

The equation 10*x^2 - 250 = 0 is already in a*x^2+b*x+c=0 form.

As the value is already arranged in a*x^2+b*x+c=0 form, we get the value of a = 10, b = 0, c = -250.

1A. Find the roots using Quadratic Formula !

  By using abc formula the value of x is both

    x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)

  As a = 10, b = 0 and c = -250,

  then the value a,b and c in the abc formula, can be subtituted.

  So x1 = (-(0) + sqrt( (0)^2 - 4 * (10)*(-250)))/(2*10) and x2 = (-(0) - sqrt( (0)^2 - 4 * (10)*(-250)))/(2*10)

  Which is the same with x1 = ( 0 + sqrt( 0+10000))/(20) and x2 = ( 0 - sqrt( 0+10000))/(20)

  Which can be turned into x1 = ( 0 + sqrt( 10000))/(20) and x2 = ( 0 - sqrt( 10000))/(20)

  We can get x1 = ( 100 )/(20) and x2 = (  - 100 )/(20)

  So we got the answers as x1 = 5 and x2 = -5

1B. Use factorization to find the root of the equation !

  10*x^2 - 250 = 0

  <=> 10 * ( x - 5 ) * ( x + 5 ) = 0

  So we got the answers as x1 = 5 and x2 = -5

1C. Use completing the square to find the root of the equation !

  10*x^2 - 250 = 0 ,divide both side with 10

  By doing so we get x^2 - 25 = 0 ,

  And the coefficient of x is 0

  We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = 0/2 = 0

  By using that fact we turn the equation into x^2  - 25 = 0

  So we will get ( x  )^2  - 25 = 0

  And it is the same with (( x  ) - 5 ) * (( x  ) + 5 ) = 0

  By using the associative law we get ( x  - 5 ) * ( x  + 5 ) = 0

  Just add up the constants in each brackets, and we get ( x - 5 ) * ( x + 5 ) = 0

  So we got the answers as x1 = 5 and x2 = -5

Answer 6

x=5