Solve for x: x^2-6x+9=0. If the solution are complex numbers then give your solutions in the usual a+bi form?

Answer 1

First, use the quadratic formula i.e. x = (-b +/- \sqrt{b^2-4ac})/2a.
So x_1 = (6 + \sqrt{36-36})/2 = 3, and the other one is the same since 36-36 = 0. So you have a root and thus you can write x^2-6x+9 = (x-3)(x-3) = (x-3)^2. Thus the only solution for this equation is x = 3.

Answer 2

question huge sort a million : For this equation x^2 + 4*x + 7 = 0 , answer here questions : A. discover the roots employing Quadratic formulation ! B. Use winding up the sq. to discover the basis of the equation ! answer huge sort a million : The equation x^2 + 4*x + 7 = 0 is already in a*x^2+b*x+c=0 variety. because of the fact the cost is already arranged in a*x^2+b*x+c=0 variety, we get the cost of a = a million, b = 4, c = 7. 1A. discover the roots employing Quadratic formulation ! by using employing abc formulation the cost of x is the two x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a) We had be attentive to that a = a million, b = 4 and c = 7, we ought to subtitute a,b,c interior the abc formulation, with thos values. So x1 = (-(4) + sqrt( (4)^2 - 4 * (a million)*(7)))/(2*a million) and x2 = (-(4) - sqrt( (4)^2 - 4 * (a million)*(7)))/(2*a million) Which make x1 = ( -4 + sqrt( sixteen-28))/(2) and x2 = ( -4 - sqrt( sixteen-28))/(2) Which make x1 = ( -4 + sqrt( -12))/(2) and x2 = ( -4 - sqrt( -12))/(2) it is the comparable with x1 = ( -4 + sqrt(12)*sqrt(-a million))/(2) and x2 = ( -4 - sqrt(12)*sqrt(-a million))/(2) considering that all of us be attentive to that sqrt(-a million) = i, So we get x1 = ( -4 + 3.46410161513775*i )/(2) and x2 = ( -4 - 3.46410161513775*i )/(2) We get following solutions x1 = -2 + a million.73205080756888*i and x2 = -2 - a million.73205080756888*i 1B. Use winding up the sq. to discover the basis of the equation ! x^2 + 4*x + 7 = 0 ,divide the two element with a million Then we get x^2 + 4*x + 7 = 0 , And the coefficient of x is 4 we ought to apply the reality that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = 4/2 = 2 next, we ought to separate the consistent to variety x^2 + 4*x + 4 + 3 = 0 And it fairly is the comparable with ( x + 2 )^2 + 3 = 0 it is the comparable with (( x + 2 ) - a million.73205080756888*i ) * (( x + 2 ) + a million.73205080756888*i ) = 0 by using beginning the brackets we can get ( x + 2 - a million.73205080756888*i ) * ( x + 2 + a million.73205080756888*i ) = 0 The solutions are x1 = -2 + a million.73205080756888*i and x2 = -2 - a million.73205080756888*i

Answer 3

(x-3)² = 0
x²-6x+9=0
delta = 6² - 4.1.9
delta = 36 - 36
delta = 0
x = (6 +/- \/0) : 2
x = 6: 2 = 3
Two equal roots.
Solution: {x elements of R | x' = x" =3}
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Answer 4

Isn't this a perfect square?

(x - 3)^2 = 0
x = 3

Answer 5

it is a perfect square!
x^2-2*3*x+3^2=o
(x-3)^2=0
x-3=0
x=3