Question

solve the equation by factoring.
14x² + 3x - 2 = 0
rewrite the equation in factored form.
□ = 0
(factor completely.)

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(14\times(-2)= -28\) and add up to \(3\). The numbers are \(7\) and \(-4\) since \(7\times(-4)= -28\) and \(7 + (-4)=3\).

Step2: Split the middle term

Rewrite the middle term \(3x\) using \(7\) and \(-4\):
\(14x^{2}+7x - 4x - 2 = 0\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((14x^{2}+7x)+(-4x - 2)=0\)
Factor out the greatest common factor from each group:
\(7x(2x + 1)-2(2x + 1)=0\)

Step4: Factor out the common binomial

Factor out \((2x + 1)\) from both terms:
\((7x - 2)(2x + 1)=0\)

Answer:

\((7x - 2)(2x + 1)\)