SOLUTION: Solve for x: x^2-10x+14=0

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Question 119140:
Solve for x: x^2-10x+14=0
Found 2 solutions by jim_thompson5910, checkley71:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2-10%2Ax%2B14=0 ( notice a=1, b=-10, and c=14)




x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A14+%29%29%2F%282%2A1%29 Plug in a=1, b=-10, and c=14



x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A14+%29%29%2F%282%2A1%29 Negate -10 to get 10



x+=+%2810+%2B-+sqrt%28+100-4%2A1%2A14+%29%29%2F%282%2A1%29 Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because %28-10%29%5E2=-10%2A-10=100.)



x+=+%2810+%2B-+sqrt%28+100%2B-56+%29%29%2F%282%2A1%29 Multiply -4%2A14%2A1 to get -56



x+=+%2810+%2B-+sqrt%28+44+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%2810+%2B-+2%2Asqrt%2811%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+=+%2810+%2B-+2%2Asqrt%2811%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%2810+%2B+2%2Asqrt%2811%29%29%2F2 or x+=+%2810+-+2%2Asqrt%2811%29%29%2F2


Now break up the fraction


x=%2B10%2F2%2B2%2Asqrt%2811%29%2F2 or x=%2B10%2F2-2%2Asqrt%2811%29%2F2


Simplify


x=5%2Bsqrt%2811%29 or x=5-sqrt%2811%29


So these expressions approximate to

x=8.3166247903554 or x=1.6833752096446


So our solutions are:
x=8.3166247903554 or x=1.6833752096446

Notice when we graph x%5E2-10%2Ax%2B14, we get:



when we use the root finder feature on a calculator, we find that x=8.3166247903554 and x=1.6833752096446.So this verifies our answer

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
X^2-10X+14=0
USING THE QUADRATIC EQUATION-x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ WE GET:
X=(10+-SQRT[-10^2-4*1*14])/2*1
X=(10+-SQRT[100-56])/2
X=(10+-SQRT44)/2
X=(10+-6.63)/2
X=(10+6.63)/2
X=16.63/2
X=8.32 ANSWER.
X=(10-6.63)/2
X=3.37/2
X=1.68 ANSWER.