Solve by completing the square. 2x^2 – 2x – 3 = 0?

Answer 1

2 ( x ² - x - 3 / 2 ) = 0
x ² - x - 3 / 2 = 0
( x ² - x + 1 / 4 ) - 1 / 4 - 3 / 2 = 0
(x - 1 / 2) ² = 6 / 4 + 1 / 4
(x - 1 / 2) ² = 7 / 4
(x - 1 / 2) = ± ( 1 / 2 ) √7
x = 1 / 2 ± ( 1 / 2 ) √7
x = (1 / 2) (1 ± √7 )

Answer 2

2x² -2x -3 = 0

take 3 to the other side

2x² -2x =3

divide throughout by the coefficient of x² ie : 2

x² -x =3/2

add the square of one half of the coefficient of x to both sides

x² -x + (1/2 * -1)² = 3/2 + (1/2 * -1)²
x² -x + (-1/2)² = 3/2 + (-1/2)²
x² -x + 1/4 = 3/2 + 1/4
x² -x + 1/4 = (6 + 1)/4
x² -x + 1/4 = 7/4
x² -x + 1/4 = (√7/2)²
the left hand side is in the form (x-a)² = x² - 2ax + a²

(x - 1/2)² = (√7/2)²
taking square roots on both sides
(x - 1/2) = ± √7/2
there are two roots for the equation given by

x - 1/2 = √7 / 2 and
x - 1/2 = - √7 /2

x = √7/2 + 1/2 = (√7+ 1)/2 and
x = -√7/2 + 1/2 = (-√7+1)/2

therefore x = (√7+ 1)/2 or (-√7+ 1)/2

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Answer 3

2x² - 2x - 3 = 0

Bring the 3 over to the other side:

2x² - 2x = 3

Factor out the 2 from the left side:

2(x² - x) = 3

Divide both sides by 2:

(x² - x) = 3/2

Add one half of the second term on the left squared to both sides:

(1 / 2)² = 1/4

(x² - x + 1/4) = 3/2 + 1/4
(x - 0.5)² = 7/4
Take the square root of both sides:

x - 0.5 = ±√7 / 2

x = 0.5 (±√7 / 2)

x = approx. 1.82288 or approx. -0.82288

Answer 4

ehh okay.
x^2-x-3/2=0
x^2-x=3/2
x^2-x-(1/2)^2=3/2
(x-1/2)^2=3/2
(square root both sides)
x-1/2=rt3/2
x= 1/2 +/- rt3/2

Answer 5

x^2 - x = 3/2
x^2 - x + (1/2)^2 = 3/2 + (1/2)^2
(x-1/2)^2 = 7/4
x-1/2 = +/-sqrt(7/4)
x = 1/2 +/- sqrt(7)/2

Answer 6

USE the quadratic formula---