## Solve quadratic equation, Algebra

Assignment Help:

Solve following equations by factoring.

a) x2 - x = 12

b) y 2 + 12 y + 36 = 0

Solution

a)      x2 - x = 12

First to solve it get everything on side of the equation and then factor.

x2 - x = 12

( x - 4) ( x + 3) = 0

Now we've got a product of two terms which is equal to zero. It means that at least one of the following must be true.

x - 4 = 0          OR                                 x + 3 = 0

x = 4               OR                                  x = -3

Note that each of these is linear equation i.e easy enough to solve.  Now we have two solutions to the equation,

x = 4 and

x = -3 .

As through linear equations we can always check our solutions through plugging the solution back into the equation.  We will check x = -3 and leave the other to you to check.

12    = 12          OK

b)      y 2 + 12 y + 36 = 0

In this case already we have zero on one side & thus we don't have to do any manipulation to the equation all that we have to do is factor.  Also, don't get excited regarding the fact that now we have y's in the equation. We won't always be dealing along with x's so don't expect to always see them.

So, let's factor this equation.

y 2 + 12 y + 36 = 0

(y + 6)2  = 0

(y + 6) ( y +6) = 0

In this we've got a perfect square.  We broke up the square to indicate that we actually do have an application of the zero factor property.  Though, we usually don't do that. Usually we will go straight to the answer from the squared part.

In this case solution to the equation is,

y = -6

We have a single value here only as opposed to the two solutions we've been getting to this point. We will frequently call this solution a double root or say that it contain multiplicity of 2 since it came from a term that was squared.

#### Finding the inverse of a function, The process for finding the inverse of a...

The process for finding the inverse of a function is a quite simple one although there are a couple of steps which can on occasion be somewhat messy.  Following is the process G

#### Methods of elimination - linear systems, Methods of elimination Example...

Methods of elimination Example 1 Solve out the given system of equations. x - 2 y + 3z = 7 2 x + y + z = 4 -3x + 2 y - 2 z = -10 Solution We will try and find

#### Frank, Have a % 56% discount have the amount of 285.13 what was the amoun...

Have a % 56% discount have the amount of 285.13 what was the amount used to get to 285.13? How did you get?

#### Properties of exponential functions, Properties of f( x ) = b x 1. The...

Properties of f( x ) = b x 1. The graph of f( x ) will always have the point (0,1).  Or put another way, f(0) = 1 in spite of of the value of b. 2. For every possible b b x

#### Algebra 2, How do I take two points, the rise and run, and produce an algeb...

How do I take two points, the rise and run, and produce an algebraic equation?

#### Algebra 2 with trig, I am supposed to put y= -2x-16x-32 in vertex form and ...

I am supposed to put y= -2x-16x-32 in vertex form and identify the vertex , axis of symmetry, and direction of opening.

76 * 10 -9

#### Exponential functions, Definition of an exponential function If b is an...

Definition of an exponential function If b is any number like that b = 0 and b ≠ 1 then an exponential function is function in the form,

#### Composition of functions, Find g(f(h(-3))). f(x) = 2x -- g(x) = -3x+4 -- h...

Find g(f(h(-3))). f(x) = 2x -- g(x) = -3x+4 -- h(x) = -2x-8

#### Exponential and radical functions, Graph each data set. Which kind of mode...

Graph each data set. Which kind of model best describes the data? {(0,3), (1,9), (2,11) (3,9), (4,3)}

### Write Your Message!  #### Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!