SOLUTION: This is from a chapter on solving a quadratic equation by compleating a square. Please help me solve. {{{(4)/(m^2-7)=1}}} Thank you.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: This is from a chapter on solving a quadratic equation by compleating a square. Please help me solve. {{{(4)/(m^2-7)=1}}} Thank you.      Log On


   

Question 211918This question is from textbook Intoductery Algebra
: This is from a chapter on solving a quadratic equation by compleating a square. Please help me solve.
%284%29%2F%28m%5E2-7%29=1
Thank you. This question is from textbook Intoductery Algebra

Found 2 solutions by drj, MathTherapy:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
This is from a chapter on solving a quadratic equation by completing a square. Please help me solve.
%284%29%2F%28m%5E2-7%29=1
Step 1. For this case completing the square was not needed. Let's get rid of the denominator by multiplying the denominator to both sides of the equation.

The equation %284%29%2F%28m%5E2-7%29=1 OR %284%29%28m%5E2-7%29%2F%28m%5E2-7%29=1%2A%28m%5E2-7%29 which will now be

%284%29=%28m%5E2-7%29

Step 2. Now let's subtract -4 from both sides of the equation.

%284-4%29=0=%28m%5E2-7-4%29

0=%28m%5E2-11%29 (note: the answer is just the m=sqrt%2811%29) plus or minus sqrt(11)



Step 3. So this is now a quadratic equation where

a=1, b=0, and c=-11 where we will use the quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Step 4. See the steps below to solve this.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-11+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A1%2A-11=44.

Discriminant d=44 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+44+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+44+%29%29%2F2%5C1+=+3.3166247903554
x%5B2%5D+=+%28-%280%29-sqrt%28+44+%29%29%2F2%5C1+=+-3.3166247903554

Quadratic expression 1x%5E2%2B0x%2B-11 can be factored:
1x%5E2%2B0x%2B-11+=+1%28x-3.3166247903554%29%2A%28x--3.3166247903554%29
Again, the answer is: 3.3166247903554, -3.3166247903554. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-11+%29



Note: Step-By-Step Videos in Pre-Algebra can be found at http://www.FreedomUniversity.Tv/courses/IntroAlgebra.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
This is from a chapter on solving a quadratic equation by compleating a square. Please help me solve.
%284%29%2F%28m%5E2-7%29=1

We proceed by completing the square to solve this equation

m%5E2+-+7+=+4 -------> Cross-multiplying
m%5E2+=+11 ------> Add 7 to both sides of equation
b = 0, so there is no halving "b" and then squaring the result, so move on to next step
sqrt%28m%5E2%29+=_%2B-sqrt%2811%29
m+=+_%2Bsqrt%2811%29_or_-sqrt%2811%29

Therefore, m = highlight_green%283.31662479%29 or highlight_green%28-3.31662479%29