SOLUTION: solve the equation using the -b +/- square root of b squared-4(a)(c)divided by 2a 1. I know the formula I just cannot figure this out. x squared = 196 Also if you can hel

Algebra ->  Linear-equations -> SOLUTION: solve the equation using the -b +/- square root of b squared-4(a)(c)divided by 2a 1. I know the formula I just cannot figure this out. x squared = 196 Also if you can hel      Log On


   

Question 117161: solve the equation using the -b +/- square root of b squared-4(a)(c)divided by 2a
1. I know the formula I just cannot figure this out.
x squared = 196
Also if you can help with another.
x squared -4x +2 = 0
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1


x%5E2=196 Start with the given equation


x%5E2-196=0 Move all of the terms to the left side

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 x%5E2-196=0 (note: since the polynomial does not have an "x" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like x%5E2%2B0%2Ax-196=0 notice a=1, b=0, and c=-196)




x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A1%2A-196+%29%29%2F%282%2A1%29 Plug in a=1, b=0, and c=-196



x+=+%280+%2B-+sqrt%28+0-4%2A1%2A-196+%29%29%2F%282%2A1%29 Square 0 to get 0



x+=+%280+%2B-+sqrt%28+0%2B784+%29%29%2F%282%2A1%29 Multiply -4%2A-196%2A1 to get 784



x+=+%280+%2B-+sqrt%28+784+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-0+%2B-+28%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%280+%2B-+28%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%280+%2B+28%29%2F2 or x+=+%28-0+-+28%29%2F2

Lets look at the first part:

x=%280+%2B+28%29%2F2

x=28%2F2 Add the terms in the numerator
x=14 Divide

So one answer is
x=14



Now lets look at the second part:

x=%280+-+28%29%2F2

x=-28%2F2 Subtract the terms in the numerator
x=-14 Divide

So another answer is
x=-14

So our solutions are:
x=14 or x=-14

Notice when we graph x%5E2-196, we get:

+graph%28+500%2C+500%2C+-24%2C+24%2C+-24%2C+24%2C1%2Ax%5E2%2B0%2Ax%2B-196%29+

and we can see that the roots are x=14 and x=-14. This verifies our answer





#2

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 x%5E2-4%2Ax%2B2=0 ( notice a=1, b=-4, and c=2)




x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29 Plug in a=1, b=-4, and c=2



x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29 Negate -4 to get 4



x+=+%284+%2B-+sqrt%28+16-4%2A1%2A2+%29%29%2F%282%2A1%29 Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because %28-4%29%5E2=-4%2A-4=16.)



x+=+%284+%2B-+sqrt%28+16%2B-8+%29%29%2F%282%2A1%29 Multiply -4%2A2%2A1 to get -8



x+=+%284+%2B-+sqrt%28+8+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%284+%2B-+2%2Asqrt%282%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%284+%2B-+2%2Asqrt%282%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%284+%2B+2%2Asqrt%282%29%29%2F2 or x+=+%284+-+2%2Asqrt%282%29%29%2F2


Now break up the fraction


x=%2B4%2F2%2B2%2Asqrt%282%29%2F2 or x=%2B4%2F2-2%2Asqrt%282%29%2F2


Simplify


x=2%2Bsqrt%282%29 or x=2-sqrt%282%29


So these expressions approximate to

x=3.41421356237309 or x=0.585786437626905


So our solutions are:
x=3.41421356237309 or x=0.585786437626905

Notice when we graph x%5E2-4%2Ax%2B2, we get:



when we use the root finder feature on a calculator, we find that x=3.41421356237309 and x=0.585786437626905.So this verifies our answer

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1. I know the formula I just cannot figure this out.
x squared = 196
x^2-196 = 0
x = [0 +-sqrt(0 - 4*196)]/2
x = [+- 28]/2
x = +14 or x= -14
-----------------------------
Also if you can help with another.
x squared -4x +2 = 0
x = [4 +- sqrt(16-4*2)]/2
x = [4 +- sqrt(8)]/2
x = 2 + sqrt2 or x = 2 - sqrt2
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Cheers,
Stan H.