How do you solve 4x^2 +4x = 15 using the quadratic formula?

2 Answers
Apr 11, 2018

x = 3/2, 5/2.

Explanation:

First Of All, Convert the Equation to It's General Form ax^2 + bx + c = 0.

So We have,

color(white)(xxx)4x^2 + 4x = 15

rArr 4x^2 + 4x - 15 = 0 [Subtract 15 from both sides.]

So, Comparing the Equation with the General Form, We get,

a = 4, b = 4, c = -15.

So, Let's Find the Discriminat.

D = b^2 - 4ac = 4^2 - 4*4*(-15) = 16 + 240 = 256

As D gt 0, we will get two roots which are real and distinct.

Now Use The Quadratic Formula or Sridhar Acharya's Rule (whatever you may call it in your country).

alpha = (-b + sqrt(D))/(2a) = (-4 + sqrt(256))/(2 * 4) = (-4 + 16)/(8) = 3/2

And beta = (-b - sqrt(D))/(2a) = (-4 - sqrt(256))/(2 * 4) = (-4 - 16)/(8) = 5/2

So, x = 3/2, 5/2

Hope this helps.

Apr 11, 2018

3/2 " or" - 5/2

Explanation:

Make the expression equal to zero:

4 x^2 + 4x - 15 = 0

The quadratic formula is:

x = (-b +- sqrt (b^2 -4 a c )) / (2a)

In our case we substitute:

a = 4, b = 4, c = -15

So that the quadratic formula becomes:

x = (-4 +- sqrt (4^2 -4 * 4 *(-15) )) / (2*4)

= (-4 +- sqrt (16 + 240 )) / (8)

= (-4 +- 16) / (8)

= 3/2 "or" - 5/2

We can also solve this by factorising (here you need to guess)

4 x^2 + 4x - 15 = 0

(2x + 5 ) (2x - 3) = 0

Then make both parenthesis equal to zero to get the same answers:

(2x + 5 ) = 0 " or " (2x - 3) = 0