Question

I need to solve by completing the square but I just can’t seem to get the correct answer, the quadratic is 2x^2- .5x-28=0

Answer 1

x - 5.19 or x = -2.67 is the correct answer.

Explanation:

Here, the given quadratic equation is:
`2x^2- 5x-28=0`

To solve it by : Completing The Square

Step : 1 Make the coefficient of leading variable x² as 1.

Divide whole equation by 2,we get:

`x^2- (5)/(2) x-14=0\\\implies x^2- (5)/(2) x = 14`

Step 2: Find the coefficient of x in the equation and DIVIDE it by 2 to HALF THE VALUE

Here, the coefficient of x = (-5/2)

Dividing ot by 2, we get the value = (-5/4)

Step 3: ADD THE SQUARE of the found value on BOTH sides.

And USE:
`(a - b)^2 = a^2 + b^2 - 2ab`

`x^2- (5)/(2) x = 14 \implies x^2- (5)/(2) x + ((5)/(4) )^2= 14 + ((5)/(4) )^2\\\implies (x -(5)/(4))^2 = 14 + (25)/(16) = (224 + 25)/(16) = (249)/(16) \\\implies (x -(5)/(4))^2 = (249)/(16) = ((15.7)/(4))^2\\ \implies (x -(5)/(4))^2 = ((15.7)/(4))^2`

Step 4: TAKE ROOT ON BOTH SIDES, we get:

`(x -(5)/(4))^2 = ((15.7)/(4))^2\\\implies (x -(5)/(4)) = \pm ((15.7)/(4))\\\implies x = ((15.7)/(4)) +((5)/(4)) = 5.19\\or, x = - ((15.7)/(4)) +((5)/(4)) = -2.67\\`

So, either x - 5.19 or x = -2.67