9x2+4=2x Solve using the quadratic formula.

Question

9x²+4=2x Solve using the quadratic formula  PLEASE RESPOND ASAP

Answer 1

Hello: I agree with the answer of Mr John K but not the last step; When I arrive to the step x1,2 _= 2 +- square roof of -140 divide by 18, I make the conversion of square roof of -140 because the negative number have not square roof and they have to be complemented by i numbers, remember i= -1. For that reason I made the decomposition in factor of 140 which is 2 power 2 time 5 time 7, after that I simplify both terms in the numerator with the denominator and the answers are: X1 = 1 + square roof of 35 time "i"(imaginary number equal to -1) divide all expression by 9 and X2 the same but in the numerator you have to subtract the square roof. I think that it is not convenient calculate the final amount. at less you need to do it

Answer 2

The quadratic formula is given ax^2 + bx + c = 0 then roots of the equation  are (-b +- sqrt(b^2-4ac)/2a. There are solvers on the web but this formula should be commited to memory. In your problem 9x^2 - 2x + 4 = 0. From the formula the roots are r1 = (2 + sqrt(4-144))/18 = (2+sqrt(-140))/18, , r2 = (2 - sqrt(4-144)/18 = (2+sqrt(-140))/18, or in summary r1 = (0.111111 + 0.65734i), r2 = (0.111111 - 0.65734i), with i == sqrt(-1) and r1,r2 roots of the quadratic equation. 

Answer 3

The trick to this is to identify a,b,c and plug into the quadratic formula

 

  Move everything away from the right hand side:

  9x²-2x+4 = 0

 

  Recall that a is the leading coefficient on the x² term, b is the leading coefficient on the x term, and c is the coefficient without any x's:

    a = 9

    b = -2

    c = 4

 

  Then get answers from the quadratic formula

    (-b +/- sqrt(b²-4ac)) / 2a 

 

  Positive root answer is:

    (--2 + sqrt(4-144))/18

    = (2 + sqrt(-140))/18

    = (2 + sqrt(-1*4*35))/18

    = (2 + 2 sqrt(35)i)/18

    = 1/9 + sqrt(35)i/9

  And this is approximately:

    0.111 + 0.657i

 

  Negative root answer is:

    = 1/9 - sqrt(35)i/9

  And this is approximately:

    0.111 - 0.657i