SOLUTION: Use the quadratic formula to solve the equation 7x^2-32x=31

Question 113973: Use the quadratic formula to solve the equation
7x^2-32x=31

Found 3 solutions by MathLover1, checkley71, jim_thompson5910:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
write an equation of the line having the following properties. is parallel to the graph of 5/4 x-3 and passes through the origin?

Use the quadratic formula to solve the equation

the roots are:

check for

�round it

check another one too

Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
7X^2-32X-31=0

X=(32+-SQRT[32^2-4*7*-31])/2*7
X=(32+-SQRT[1024+868])/14
X=(32+-SQRT1892)/14
X=(32+-43.497)/14
X=(32+43.497)/14
X=75.497/14
X=5.39 ANSWER.
X=(32-43.497)/14
X=-11.97/14
X=-.82 ANSWER.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation

Subtract 31 from both sides

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=7, b=-32, and c=-31

Negate -32 to get 32

Square -32 to get 1024 (note: remember when you square -32, you must square the negative as well. This is because .)

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 7 to get 14

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our solutions are:
or

Notice when we graph , we get:

when we use the root finder feature on a calculator, we find that and .So this verifies our answer

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