SOLUTION: solve the equation by completeing the square: 7x^2+10x=-2

Question 548975: solve the equation by completeing the square:
7x^2+10x=-2
Found 3 solutions by mananth, josmiceli, mathie123:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
7x^2+10x=-2
/7
x^2+(10/7)x= -2/7
7 X^2 + 10 x = -2
/7
1 X^2 + 10/7 x+b= - 2/7
Calculate third term (b)
2 * b * 1 = 10/7
2 b = 10/7
b= 10/7 / 2
b= 5/7
b^2= 25/49

x^2 + 10/7 x+ 25/49 =- 2/7+ 25/49
(x+ 5/7 )^2= 11/49
( x+ 5/7) = sqrt(11)/7
x= - 5/7 +/- sqrt(11)/7

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

Divide both sides by

Take 1/2 of the coefficient of ,
square it, and add it to both sides

Take the square root of both sides

Here's a plot of equation:

Answer by mathie123(224)   (Show Source): You can put this solution on YOUR website!

We will first put everything on one side of the equation (as in most classes, students are most familiar with completely the square when it is in the form ax^2+bx+c
this gives us:

Now we need to make the constant in front of x^2 1, so we will factor out a 7 from our first two terms:

Now the rules for completing the square say we must take the constant in front of the x and square one half of this number and add and subtract this number.
So our constant is 10/7. One half of 10/7 is
10/7*1/2=10/14
and this squared is
(10/14)^2=(5/7)^2=25/49
So we will add and subtract this number (so essentially we are adding 0 to our equation, which does not change it).

We will now take our -25/49 out of the bracket (remembering to multiply it by 7 when we take it out). this leaves:

Almost there....
We will complete the square inside of the brackets. Essentially we just write it in the form (x+a)^2 where a is 1/2 of the constant in front of the x term originally (we found this was 10/14=5/7
So we have:

Now it is just solving for x, so let's isolate x:

This can be simplified on your calculator... but I will leave that to you.
Hopefully this helps... let me know if you are still unsure.

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