SOLUTION: How would you solve this equation? a^2-3=2a

Click here to see ALL problems on Equations

Question 124943: How would you solve this equation?
a^2-3=2a
Found 3 solutions by jim_thompson5910, stanbon, bucky:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!

Start with the given equation

Subtract 2a from both sides.

Rearrange the terms

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for a in each case

So our answer is
or

Notice if we graph (just replace a with x) we can see that the roots are and . So this visually verifies our answer.

Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
solve this equation
a^2-3=2a
------------
a^2-2a-3 = 0
Factor to get:
(a-3)(a+1) = 0
a-3 =0 or a+1=0
a = 3 of a = -1
=================
Cheers,
Stan H.

Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website!
Given:
.
a^2 - 3 = 2a
.
To solve this, begin by getting it into a standard quadratic form in which the right side
of the equation equals zero. To do this you just need to subtract 2a from both sides of
the equation. This subtraction makes the equation become:
.
a^2 - 2a - 3 = 0
.
The left side of this equation can be factored into two binomials. When you factor the left side
the equation is transformed to:
.
(a - 3)(a + 1) = 0
.
[Notice that if you multiply out the two binomials factors on the left side you get back to
a^2 - 2a - 3 = 0]
.
This equation will be true if either of the two binomial factors is equal to zero because
multiplying the two factors (when one of them is zero) will make the entire left side of the
equation be equal to zero and therefore the left side will be equal to the zero on the right side.
.
So, one at a time set the two factors equal to zero. First:
.
a - 3 = 0
.
Solve for a by adding 3 to both sides of this equation and you get a = 3.
.
Next, set the second factor equal to zero:
.
a + 1 = 0
.
Solve for a by subtracting 1 from both sides to get:
.
a = -1
.
That is the second answer. The two answers are a = 3 and a = -1
.
You can check these answers by returning to the original problem:
.
a^2 - 3 = 2a
.
and, one at a time substitute the answers to see if the left side of the equation will
equal to the right side.
.
Check a = 3 by substituting 3 for a in the original problem and you get:
.
3^2 - 3 = 2*3
.
Square the 3 and subtract 3 from it on the left side and multiply out the right side to get:
.
9 - 3 = 6
.
This simplifies to 6 = 6 which tells us that a = 3 is a good answer.
.
Next check a = -1 by substituting -1 for a in the original problem to get:
.
(-1)^2 - 3 = 2*(-1)
.
This reduces to:
.
1 - 3 = -2
.
-2 = -2
.
So this answer for a checks also. Both our answers [a = 3 and a = -1] are correct.
.
Hope this helps you to understand the problem.
.