nicely, using the quatratic formula in all probability isn't the least complicated thank you to remedy, yet once you need to: use the quadratic formula (-b (plus or minus)((sq. root) b^2-4ac))/2a to confirm a, it is the coffefficient of X^2. for this reason, on your case, it is one million. B is the coefficient of x. on your case, it is -8. and c is the the quantity with out variable attatched. for this reason, it is sixteen. Now, all you need to do is replace one and all of those variables into the formula. 8 (plus or minus) ((the sq. root) sixty 4-4(sixteen)) / 2(one million). Simplified, 8 (plus or minus) 0 / 2. for this reason, the respond x=4. do no longer believe me? verify the respond 4^2 -8(4) + sixteen =0 Yay, it fairly works
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Verified answer
No, this does not factor. In order to factor you would need two numbers that multiply to give you -4 and add to -8, and there are no such numbers.
that's it! ;)
It cannot be factored over the rational numbers:
However if you know how to complete the square you will have tow factors over the real numbers;
x^2 - 8x = 4
x^2 - 8x + 16 = 20
(x-4)^2 = 20
x- 4 = ± √20 = ±2√5
x = 4±2√5
If for some reason you still wanted to factor the factors are:
(x - 4 +2√5)(x - 4 -2√5)
x² – 8x – 4 = 0
(x² – 8x + 16) – (20) = 0
(x – 4)² – (√20)² = 0
[(x – 4) – (√20)][(x – 4) + (√20)]
(x – 4 – √20)(x – 4 + √20) = 0
(x – 4 – 2 √5)(x – 4 + 2√5) = 0
x = (x – 4 – 2 √5) or = (x – 4 + 2√5)
-------------
8x 2-x 4
x^2 -8x – 4 = 0
(x^2 -8x +16) -16 -4 = 0
(x - 4)^2 - 20 = 0
(x - 4 - 2sqrt(5))(x - 4 + 2sqrt(5)) = 0
the equation
xx-8x-4=0 has the solutions
x(1)=4+sqrt(20)
x(2)=4-sqrt(20)
ans so
xx-8x-4=[x-x(1][x-x(2)] (2)
check that (2) is an identity
Yes. Use the Quadratic formula:
-b + or - the square root of b squared - 4ac divided by 2a
standard form is ax2 + bx + c=0 so in your case, a=1 b=-8 and c=-4
so -(-8) + or - (the square root of -8 squared - 4(1)(-4)) divided by 2(1)
--> 8 + or minus (the square root of 64 - (-16)) divided by 2
--> 8 + or - (the square root of 80)/2
--> x = 8.5 or x= -.47
nicely, using the quatratic formula in all probability isn't the least complicated thank you to remedy, yet once you need to: use the quadratic formula (-b (plus or minus)((sq. root) b^2-4ac))/2a to confirm a, it is the coffefficient of X^2. for this reason, on your case, it is one million. B is the coefficient of x. on your case, it is -8. and c is the the quantity with out variable attatched. for this reason, it is sixteen. Now, all you need to do is replace one and all of those variables into the formula. 8 (plus or minus) ((the sq. root) sixty 4-4(sixteen)) / 2(one million). Simplified, 8 (plus or minus) 0 / 2. for this reason, the respond x=4. do no longer believe me? verify the respond 4^2 -8(4) + sixteen =0 Yay, it fairly works
yes it can be factored. if u complete the square the answer is ((x-4)^2)-20 which is a simpler version of the original form.