I can't figure out how to do this math problem. Find the solution set in a + bi form x(squared) + 6x + 12 = 0

Question

I don't understand how to solve it, becuase their are no factors of 12 that add to 6. Any help is much apprecaited. Thanks

Answer 1

Some quadratic equations cannot be factored directly because they have irrational factors (in other words, factors of the form a + bi where b≠0).
To find the factors for these equations you need to use the quadratic formula. If you don't know what that is, or don't know how to use it, you can read about it here: http://purplemath.com/modules/quadform.htm

Just plug the numbers from your equation in and solve. You should come up with an answer that looks something like this: a±(√b)i

Answer 2

Use the two ending up the sq. or quadratic formula question type a million : For this equation x^2 + 6*x + 12 = 0 , answer here questions : A. discover the roots employing Quadratic formula ! B. Use ending up the sq. to discover the muse of the equation ! answer type a million : The equation x^2 + 6*x + 12 = 0 is already in a*x^2+b*x+c=0 form. because of the fact the fee is already arranged in a*x^2+b*x+c=0 form, we get the fee of a = a million, b = 6, c = 12. 1A. discover the roots employing Quadratic formula ! Use the formula, x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a) As all of us understand that a = a million, b = 6 and c = 12, we ought to subtitute a,b,c interior the abc formula, with thos values. So we get x1 = (-(6) + sqrt( (6)^2 - 4 * (a million)*(12)))/(2*a million) and x2 = (-(6) - sqrt( (6)^2 - 4 * (a million)*(12)))/(2*a million) which could be became into x1 = ( -6 + sqrt( 36-40 8))/(2) and x2 = ( -6 - sqrt( 36-40 8))/(2) Which make x1 = ( -6 + sqrt( -12))/(2) and x2 = ( -6 - sqrt( -12))/(2) which could be became into x1 = ( -6 + sqrt(12)*sqrt(-a million))/(2) and x2 = ( -6 - sqrt(12)*sqrt(-a million))/(2) As sqrt(-a million) = i, So we get x1 = ( -6 + 3.46410161513775*i )/(2) and x2 = ( -6 - 3.46410161513775*i )/(2) So we've the solutions x1 = -3 + a million.73205080756888*i and x2 = -3 - a million.73205080756888*i 1B. Use ending up the sq. to discover the muse of the equation ! x^2 + 6*x + 12 = 0 ,divide the two facet with a million So we get x^2 + 6*x + 12 = 0 , because of the fact of this the coefficient of x is 6 we ought to apply the undeniable fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = 6/2 = 3 So we've make the equation into x^2 + 6*x + 9 + 3 = 0 which could be became into ( x + 3 )^2 + 3 = 0 which could be became into (( x + 3 ) - a million.73205080756888*i ) * (( x + 3 ) + a million.73205080756888*i ) = 0 by ability of establishing the brackets we can get ( x + 3 - a million.73205080756888*i ) * ( x + 3 + a million.73205080756888*i ) = 0 So we've been given the solutions as x1 = -3 - a million.73205080756888*i and x2 = -3 + a million.73205080756888*i

Answer 3

x^2 + 6x + 12 = 0
Subtract 12 from both sides :
x^2 + 6x = -12
Calculate half of the 6 (= 3), then square it (3^2 = 9).
Now add this 9 to both sides :
x^2 + 6x + 9 = -12 + 9 = -3
The left-hand side is now a square :
(x + 3)^2 = -3
Take the square root of both sides :
x + 3 = ± sqrt(-3) = ± sqrt(3)*i
Subtract 3 from both sides :
x = -3 ± sqrt(3)*i, which is now in the form a ± bi.
This method is called "Completing the Square".

Answer 4

so x^2+6x+12 =0

determinant is 36-4*12 = -12 = -1*12 and the square root of this is square root of -1 *square root of 12 = i*square root of 12
squre root of 12 = 2*square root 3
one solution is x1 =( -6-2*i*square root 3)/2 = -3-i*square root3

other solution is
x1 =( -6+2*i*square root 3)/2 = -3+i*square root3

Answer 5

Use the quadratic equation. The answer is a complex number. If your teacher hasn't explained complex numbers, you shouldn't be getting an assignment like this. If they have explained complex numbers, then you shouldn't have any problems with solving it or understanding that the answers are
-3 ± i√3

Doug