SOLUTION: Good Morning Tutor, Could you tell me if I have these problems correct? Solve: x^2 + 7x - 1 = 0 is (-6 +- sqrt of 50 / 2) Solve by completeing the square: 2x

Question 105112: Good Morning Tutor,
Could you tell me if I have these problems correct?
Solve:
x^2 + 7x - 1 = 0 is (-6 +- sqrt of 50 / 2)
Solve by completeing the square:
2x^2 + 8x - 5 = 0 is (4 +- sqrt of 26 / 2)
Thank you for your help this morning.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

this is how you need to do it:
1.

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=7, and c=-1

Square 7 to get 49

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So the solutions are:

or

Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

Start with the given equation

Add to both sides

Factor out the leading coefficient

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation

Now factor to get

Distribute

Multiply

Now add to both sides to isolate y

Combine like terms

Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor.

Check:

Notice if we graph the original equation we get:

Graph of . Notice how the vertex is (,).

Notice if we graph the final equation we get:

Graph of . Notice how the vertex is also (,).

So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.

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