solve for X in simplest a + bi form?

Question

4xsquared +17= 4X

4X^2+17=4X

Answer 1

4x² + 17 = 4x

Put everything on the left by subtracting 4x from both sides:
4x² - 4x + 17 = 0

Now use the quadratic formula to solve...
x = [ -b ± sqrt( b² - 4ac ) ] / 2a

a = 4
b = -4
c = 17

x = [ -(-4) ± sqrt( (-4)² - 4(4)(17) ) ] / 2(4)
x = [ 4 ± sqrt( 16 - 272 ) ] / 8
x = [ 4 ± sqrt( -256 ) ] / 8
x = [ 4 ± sqrt( 256 ) * sqrt(-1) ] / 8
x = ( 4 ± 16i ] / 8
x = 4/8 ± 16i/8
x = ½ ± 2i

Answer 2

So the equation is: 4x^2 + 17 = 4x

First you have to put the equation in the form of the general quadratic equation: ax^2 + bx + c = 0

In order to do that subtract 4x from both sides:

4x^2 -4x + 17 = 0

Now use the quadratic formula: [-b +- {(b^2-4ac)}^.5]/2a

Fill in the numbers: [-(-4) +- {((-4)^2-4*4*17)}^.5]/2*4
Simplifying the numbers in the square root you get:
-256.

The square root of a negative number is always imaginary; therefore, the solution is going to be complex (as you stated in the question). Complex numbers are stated in the form a + bi. A is known as the real part while b is known as the imaginary part.

The square root of -256 is the square root of 256 times i. The square root of 256 is 16 so the square root of -256 is 16i.

Put this back into the equation: 4 +- 16i is the numerator. 8 is the denominator. The solution is 4/8 +- 16i/8 . Simplify that to get 1/2 +- 2i.

So the solution is: 1/2 +- 2i

Splitting it up gives you : 1/2 + 2i
1/2 - 2i

Answer 3

complete the sqaure 9(x -3)^2 +4 9 we take out from 9x^2-54x so we get x^2 -6x we then complete the sq. (x+(b/2)) the place b is now -6x so we get so some distance 9(x -3)^2 in case you distinctive out the bracket we get 9x^2 -54x +80 one we desire 80 5 so we upload 4 subsequently we get 9((x-3)^2) +4 to clean up for x we rearrange start up with the 4 so we get 9(x-3)^2 = -4 this is going to supply 2 complicated roots (x-3)^2 = (-4/9) x-3=+-sqrt(-4/9) x= +-sqrt(-4/9)+3 i = sqrt(-a million) so we've x = +-sqrt(4/9)i+3 or 3+-sqrt(4/9)i

Answer 4

4x^2 - 4x + 17 (ax^2 + bx + c)

Delta = b^2 - 4ac = 256

Solution = [-b +/- sqrt(delta)] / 2a

Ans : 20/8 OR -12/8

Answer 5

if you mean a+bi as a complex number, it would be difficult because it has a real answer x=1/2
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sorry i confused the +/- signs the answers are 1/2 + 2i and 1/2 - 2i

Answer 6

a:=4
b:=-4
c=17

x1=(-b+sqr(b^2-4ac))/2a
x2=(-b-sqr(b^2-4ac))/2a

==>
x1= (4+sqrt(16-272))/8 =0.5+2i
x2= (4-sqrt(16-272))/8 =0.5-2i

Answer 7

.5 +- 2i