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

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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) About Me  (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
7x%5E2-32x=31
7x%5E2-32x-31=0
the roots are:
x%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29


x%5B1%2C2%5D=%2832+%2B-+sqrt%281024+%2B+868%29%29+%2F+14
x%5B1%2C2%5D=%2832+%2B-+sqrt+%281892%29%29+%2F+14
x%5B1%2C2%5D=%2832+%2B-+43.5+%29%2F+14

x%5B1%5D=%2832+%2B+43.5%29+%2F+14
x%5B1%5D=+75.5%2F+14
x%5B1%5D=+5.39
x%5B2%5D=%2832+-+43.5%29+%2F+14
x%5B2%5D=-11.5+%2F+14
x%5B2%5D=-0.82

check for x%5B1%5D=+5.39
7x%5E2-32x=31
7%285.4%29%5E2-32%285.4%29=31
7%2829.1%29-32%285.4%29=31
203.7-+172.8+=+31
30.9=+31…round it
31+=+31

check another one too

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
7X^2-32X-31=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
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) About Me  (Show Source):
You can put this solution on YOUR website!
7x%5E2-32x=31 Start with the given equation


7x%5E2-32x-31=0 Subtract 31 from both sides

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


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve 7%2Ax%5E2-32%2Ax-31=0 ( notice a=7, b=-32, and c=-31)




x+=+%28--32+%2B-+sqrt%28+%28-32%29%5E2-4%2A7%2A-31+%29%29%2F%282%2A7%29 Plug in a=7, b=-32, and c=-31



x+=+%2832+%2B-+sqrt%28+%28-32%29%5E2-4%2A7%2A-31+%29%29%2F%282%2A7%29 Negate -32 to get 32



x+=+%2832+%2B-+sqrt%28+1024-4%2A7%2A-31+%29%29%2F%282%2A7%29 Square -32 to get 1024 (note: remember when you square -32, you must square the negative as well. This is because %28-32%29%5E2=-32%2A-32=1024.)



x+=+%2832+%2B-+sqrt%28+1024%2B868+%29%29%2F%282%2A7%29 Multiply -4%2A-31%2A7 to get 868



x+=+%2832+%2B-+sqrt%28+1892+%29%29%2F%282%2A7%29 Combine like terms in the radicand (everything under the square root)



x+=+%2832+%2B-+2%2Asqrt%28473%29%29%2F%282%2A7%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%2832+%2B-+2%2Asqrt%28473%29%29%2F14 Multiply 2 and 7 to get 14

So now the expression breaks down into two parts

x+=+%2832+%2B+2%2Asqrt%28473%29%29%2F14 or x+=+%2832+-+2%2Asqrt%28473%29%29%2F14


Now break up the fraction


x=%2B32%2F14%2B2%2Asqrt%28473%29%2F14 or x=%2B32%2F14-2%2Asqrt%28473%29%2F14


Simplify


x=16+%2F+7%2Bsqrt%28473%29%2F7 or x=16+%2F+7-sqrt%28473%29%2F7


So these expressions approximate to

x=5.39265188156165 or x=-0.821223310133078


So our solutions are:
x=5.39265188156165 or x=-0.821223310133078

Notice when we graph 7%2Ax%5E2-32%2Ax-31, we get:



when we use the root finder feature on a calculator, we find that x=5.39265188156165 and x=-0.821223310133078.So this verifies our answer