2w^2 + 20w + 51 = (w + 6)^2
If there is more than one solution than write them all
2007-03-09 16:09:24 · 13 answers · asked by I can help 1 in Science & Mathematics ➔ Mathematics
2w^2 +20w +51 = w^2+12W+36
w^2 +8w + 15=0
(w + 5) (w + 3) = 0
then
w=-3 or -5
2007-03-09 16:12:55 · answer #1 · answered by Anonymous · 0⤊ 1⤋
2w² + 20w + 51 = (w + 6)²
2w² + 20w + 51 = w² + 2*w*6 + 36
2w² - w² + 20w - 12w + 51 - 36 = 0
w² + 8w + 15 = 0
(w + 3)(w + 5) = 0
Solution: {w belongs to R | w = -3 or w = -5}
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2007-03-09 16:21:55 · answer #2 · answered by aeiou 7 · 0⤊ 0⤋
2w^2 + 20w + 51 = (w + 6)^2
2w^2 + 20w + 51 = w^2 + 36 + 12w
w^2 + 8w + 15 = 0
w^2 + 3w + 5w + 15 = 0
w(w + 3) + 5(w + 3) = 0
(w + 5)(w + 3) = 0
Either w + 5 = 0
or w + 3 = 0
Set each expression to zero to get the two values of w that will satisfy the equation.
w + 5 = 0
w = -5
w + 3 = 0
w = -3
w = -5 , -3
Substitute any of the values. The equation will be satisfied.
2007-03-09 16:16:57 · answer #3 · answered by Akilesh - Internet Undertaker 7 · 0⤊ 0⤋
2w² + 20w + 51 = (w + 6)²
2w² + 20w + 51 = w² + 12w + 36
w² + 8w + 15 = 0
(w + 5)(w + 3) = 0
w+5=0 or w+3=0
w=-5 or w=-3
2007-03-09 17:43:18 · answer #4 · answered by Adrianne G. 2 · 0⤊ 0⤋
2w^2 + 20w + 51 = (w + 6)^2
2w^2 + 20w + 51 = w^2 + 12w + 36
w^2 + 8w +15 = 0
factoring:
(w+5)(w+3) = 0
w+5 = 0
w = -5 ...sol. 1
w+3 = 0
w = -3 ... sol . 2
to check:
if w= -5
2w^2 + 20w + 51 = (w + 6)^2
2(-5)^2 + 20(-5) + 51 = (-5+6)^2
2(25) - 100 + 51 = (-1)^2
50 - 100 + 51 = 1
101 -100 = 1
1 = 1 ..ok
if w = -3
2w^2 + 20w + 51 = (w + 6)^2
2(-3)^2 + 20(-3) + 51 = (-3+6)^2
2(9) - 60 + 51 = (3)^2
18 - 60 + 51 = 9
69 -60 = 9
9 = 9 ..ok
2007-03-09 16:16:49 · answer #5 · answered by datz 2 · 0⤊ 0⤋
2w^2 + 20w + 51 = (w + 6)^2
2w^2 + 20w + 51 = w^2 + 12w + 36
w^2 + 8w + 15 = 0
(w + 5) (w + 3) = 0
w = -5 or w = -3
2007-03-09 16:15:03 · answer #6 · answered by Edgard L 2 · 0⤊ 0⤋
2w^2 + 20w + 51 = (w + 6)^2
2w^2 + 20w + 51 = w^2 + 12w + 36
w^2 + 8w + 15 = 0
(w + 3)(w + 5) = 0
w = -3, -5
2007-03-09 16:14:18 · answer #7 · answered by Anonymous · 0⤊ 0⤋
simplify the other side out:
2w^2 + 20w + 51 = w^2 + 12w + 36
Subtract:
w^2 + 8w + 15 = 0
(w+3)(w+5) = 0
w = -3,-5 :)
2007-03-09 16:13:29 · answer #8 · answered by Bob R. 6 · 0⤊ 0⤋
Answer: w=-5 or -3
2w^2+20w+51=(w+6)^2
2w^2+20w+51=w^2+12w+36
w^2+8w+15=0
(w+3)(w+5)=0
w+3=0
w= -3
and
w+5=0
w= -5
2007-03-09 16:21:50 · answer #9 · answered by Fresh 2 · 0⤊ 0⤋
2w^2 + 20w + 51 = (w + 6)^2
or,2w^2+ 20w + 51 =w^2+12w+36
or,2w^2-w^2+20w-12w+51-36=0
or,w^2+8w+15=0
or,w^2+3w+5w+15=0
or,w(w+3)+5(w+3)=0
or,(w+3)(w+5)=0
i.e. either w+3=0 so,w= -3
or,w+5=0 so w= -5
ans:w= -5 or -3
2007-03-09 16:18:11 · answer #10 · answered by Anonymous · 0⤊ 0⤋