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

Answer:

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

Step-by-step 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:

$x^2- \frac{5}{2} x-14=0\\\implies x^2- \frac{5}{2} x = 14$

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: $(a - b)^2 = a^2 + b^2 - 2ab$

$x^2- \frac{5}{2} x = 14 \implies x^2- \frac{5}{2} x + (\frac{5}{4} )^2= 14 + (\frac{5}{4} )^2\\\implies (x -\frac{5}{4})^2 = 14 + \frac{25}{16} = \frac{224 + 25}{16} = \frac{249}{16} \\\implies (x -\frac{5}{4})^2 = \frac{249}{16} = (\frac{15.7}{4})^2\\ \implies (x -\frac{5}{4})^2 = (\frac{15.7}{4})^2$

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

$(x -\frac{5}{4})^2 = (\frac{15.7}{4})^2\\\implies (x -\frac{5}{4}) = \pm (\frac{15.7}{4})\\\implies x = (\frac{15.7}{4}) +(\frac{5}{4}) = 5.19\\or, x = - (\frac{15.7}{4}) +(\frac{5}{4}) = -2.67$

So, either x - 5.19 or x = -2.67