How do you solve #4x^2 + 4x - 3 = 0# by factoring?

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Answer 1 · 2015-08-12T06:36:48

The solutions for the equation are
#color(blue)(x=-3/2, x=1/2#

#4x^2+4x−3#

We can Split the Middle Term of this expression to factorise it and thereby find the solutions.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 4*(-3) = -12#
and
#N_1 +N_2 = b = 4#

After trying out a few numbers we get #N_1 = 6# and #N_2 =-2#
#6*(-2) = -12#, and #6+(-2)= 4#

#4x^2+color(blue)(4x)−3 =4x^2-color(blue)(2x +6x)−3 #

#=2x(2x-1) +3(2x-1)#

#color(blue)((2x+3)(2x-1)# is the factorised form of the expression.

Now we can equate each of the two factors to zero and find the solutions.

#2x+3 = 0, color(blue)(x=-3/2#
#2x-1=0, color(blue)(x=1/2#