Question

solve this quadratic equation by completing the square method.

Answer 1

Hope it helps u...........

Answer 2

Given Equation is 5x^2 = 4x + 7.

(i) Write in Standard form

⇒ 5x^2 - 4x - 7 = 0

(ii) Divide by 5 on both sides

⇒ x^2 - (4/5)x - (7/5) = 0.

(iii) Shift constant term to RHS

⇒ x^2 - (4/5)x = (7/5)

(iv) Add the square of one half of the coefficient of x i.e (4/10) on both sides.

⇒ x^2 - (4/5)x + (4/10)^2 = (7/5) + (4/10)^2

⇒ (x - 4/10)^2 = (7/5) + (16/100)

⇒ (x - 4/10)^2 = (39/25)

Take Square root on both sides, we get

⇒ (x - 4/10) = √(39/25)

⇒ (x - 2/5) = √(39/25)

⇒ (x - 2/5) = √39/5

--------------------------------------------------------------------------------------------------------

Now,

(i)

⇒ (x - 2/5) = (√39)/(5)

⇒ x = (√39 + 2)/5.

(ii)

⇒ (x - 2/5) = -(√39)/5

⇒ x = (-√39 + 2)/5.

Therefore, the solution set is:

⇒ {(2 + √39)/5, (2 - √39)/5}

Hope this helps!