Question

How do you solve \[4{x^2} + 4x - 3 = 0\] by factoring?

Answer 1

Hint: Given the problem above is in the form of a quadratic equation. In order to solve this we will split the middle term in such a way that the terms on adding will give the middle term c and on multiplying will give the multiplication of the first and third term. And then we will take the common terms and can find the values of x that are the roots of this equation above.

Complete step by step answer:
Given that, the equation is \[4{x^2} + 4x - 3 = 0\]
We are asked to solve the equation using the factorization method.
So we will split the middle term.
\[ \Rightarrow 4{x^2} - 2x + 6x - 3 = 0\]
Taking 2x common from first two terms and 3 common from last two terms.
\[ \Rightarrow 2x(2x - 1) + 3(2x - 1) = 0\]
Now separating the brackets as,
\[ \Rightarrow 2x - 1 = 0or2x + 3 = 0\]
Transposing the constants,
\[ \Rightarrow 2x = 1or2x = - 3\]
Taking the variable on one side,
\[ \Rightarrow x = \dfrac{1}{2}orx = \dfrac{{ - 3}}{2}\]
Thus values of x that are the roots of the equation above are, \[x = \dfrac{1}{2}\] or \[x = \dfrac{{ - 3}}{2}\] .

Note:
Note that generally we use the factorization method easily when the coefficient of the first term is 1. But we also can use it though the coefficient is any nonzero number. Quadratic equations can be solved using different methods like Completing square method and quadratic formula.