Solve the quadratic equation by factoring. 2x^2+5x+3=0

Question

Solve the quadratic equation by factoring. 2x^2+5x+3=0

in progress 0
Trung Dũng 2 months 2021-07-24T17:39:34+00:00 2 Answers 2 views 0

Answers ( )

    0
    2021-07-24T17:41:23+00:00

    Answer:

    -0.33 repeating

    Step-by-step explanation:

    2x^2=4x

    4x+5x+3=0

    combine like terms

    9x + 3 = 0

    subtract 3 from both sides

    9x = -3

    divide 9 both sides to get the variable by itself

    x = -0.33 repeating

    0
    2021-07-24T17:41:27+00:00

    Answer:

    x_1=-\frac{3}{2} \\\\x_2=-1

    Step-by-step explanation:

    the general fromula is

    (ax+b)(cx+)d)\\\\=acx^{2} +(ad+bc)x+bd

    so we need that

    ac=2\\\\ad+bc=5\\\\bd=3

    for ac = 2

    we only have 2 and 1

    so let’s say

    a=2\\\\c=1

    so we now have

    (2x+b)(x+d)\\\\2x^{2} +(2d+b)x+bd\\\\

    and for bd = 3

    we only have 3 and 1

    but we need to

    2d +b = 5

    so we can have

    b=3

    and

    d=1

    so the factorized form is

    (2x+3)(x+1)

    so we come back to

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

    so here we have two cases

    Case 1

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

    Case 2

    (x+1)=0\\\\x+1=0\\\\x=-1

    so those are our solutions

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )