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GrogVix [38]
2 years ago
5

class="latex-formula">

Show Work!

Solve by factoring, please!
Mathematics
1 answer:
melamori03 [73]2 years ago
5 0

Answer:

x=-\frac{3}{2},-1

Step-by-step explanation:

2x^2+5x+3=0

Split the second term (5x) into two terms. Multiply the coefficient of the first term (2) by the constant term (3):

2*3=6

Find which two numbers add up to 5 and multiply into 6:

3+2=5\\3*2=6\\3,2

Split 5x as the sum of 3x and 2x:

2x^2+3x+2x+3

Now factor out a common term for the first 2 terms:

2x^2+3x\\x(2x+3)

And do the same for the last 2 terms:

2x+3\\1(2x+3)

Re-insert:

x(2x+3)+1(2x+3)=0

Factor out the common term 2x+3 and insert the values in front of the parentheses (x and 1):

(2x+3)(x+1)=0

Separate the parentheses and equal them to 0. Solve for x:

2x+3=0\\2x+3-3=0-3\\2x=-3\\\\\frac{2x}{2}=\frac{-3}{2}\\\\  x=-\frac{3}{2}

and

x+1=0\\x+1-1=0-1\\x=-1

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