Solving Quadratic Equations

There are three ways in Orimath Quadratic Solver available for you to use. In the problem presented to you, you might be asked to use either quadratic formula, factorization or completing the square. Orimath Quadratic Solver can show you how to use any of them to solve a quadratic polynomial equation.

All you have to do is to check any check boxes related to solving quadratic equation ( see the picture above ). Then click as HTML to tell Orimath Quadratic Solver to solve the problem for you and tell you the steps required to get the answer.

Answer by Orimath Quadratic Solver :

Question Number 1 :
For this equation x² + 5x + 4 = 0 , 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 :
The equation x² + 5x + 4 = 0 is already in ax²+bx+c=0 form.
As the value is already arranged in ax²+bx+c=0 form, we get the value of a = 1, b = 5, c = 4.

1A . Find the roots using Quadratic Formula ! Back To Question

By using abc formula the value of x as defined by

x_[1,2] =

-b		(b²-4ac)

2a

Since a = 1, b = 5 and c = 4,

we just need to subtitute the value of a,b and c in the abc formula.

So x_[1,2] =	- (5)	(5)² - 4 (1) (4) )

	2 (1)

Which produce x_[1,2] =	-5	(25 - 16)

	2

So x_[1,2] =	-5	9

	2

We got x₁ = ( -5 + 3 )/(2) and x₂ = ( -5 - 3 )/(2)

So we got the answers as x₁ = -1 and x₂ = -4

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

x² + 5x + 4 = 0 , factorize the left hand side.

( x + 1 ) ( x + 4 ) = 0

We get following answers x₁ = -1 and x₂ = -4

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

x² + 5x + 4 = 0 ,divide both side with 1

Which result in x² + 5x + 4 = 0 ,

The coefficient of x is 5

We have to use the fact that ( x + q )² = x² + 2qx + q² , assume that q = 5/2 = 2.5 , and q² = (2.5)² = 6.25

Next, we have to separate the constant to form x² + 5x + 6.25 - 2.25 = 0

And it is the same with ( x + 2.5 )² - 2.25 = 0

Which can be turned into (( x + 2.5 ) - 1.5 ) (( x + 2.5 ) + 1.5 ) = 0

By opening the brackets we will get ( x + 2.5 - 1.5 ) ( x + 2.5 + 1.5 ) = 0

Do the addition/subtraction, and we get ( x + 1 ) ( x + 4 ) = 0

So we have the answers x₁ = -1 and x₂ = -4

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