How do you solve h^2=-3h+54h2=−3h+54?

3 Answers
Mark D.
Mar 30, 2018

h =-9 or h = 6h=−9orh=6

Explanation:

Rearrange to get

h^2 + 3h - 54 = 0h2+3h−54=0

Factorise

( h+ 9)(h - 6) = 0(h+9)(h−6)=0

h + 9 = 0 or h- 6 = 0h+9=0orh−6=0

h = - 9 or h =6h=−9orh=6

Jim G.
Mar 30, 2018

h=-9" or "h=6h=−9 or h=6

Explanation:

"arrange the equation in standard form"arrange the equation in standard form

rArrh^2+3h-54=0larrcolor(blue)"in standard form"⇒h2+3h−54=0←in standard form

"the factors of - 54 which sum to + 3 are + 9 and - 6"the factors of - 54 which sum to + 3 are + 9 and - 6

rArr(h+9)(h-6)=0⇒(h+9)(h−6)=0

"equate each factor to zero and solve for h"equate each factor to zero and solve for h

h+9=0rArrh=-9h+9=0⇒h=−9

h-6=0rArrh=6h−6=0⇒h=6

Soumalya Pramanik
Mar 30, 2018

h = -9, 6h=−9,6.

Explanation:

We have,

color(white)(xxx)h^2 = -3h + 54×xh2=−3h+54

rArr h^2 + 3h - 54 = cancel(-3h) cancel(+ 54) cancel(+ 3h) cancel(- 54) [Add 3h - 54 to both sides]

rArr h^2 + 3h - 54 = 0

rArr h^2 + (9 - 6)h - 54 = 0 [Break 3 as 9 - 6]

rArrh^2 + 9h - 6h - 54 = 0

rArr h(h + 9) - 6(h + 9) [Group Like Terms]

rArr (h + 9)(h - 6) = 0 [Group Again]

So, If,

h+ 9 = 0 rArr h = -9

and if,

h - 6 = 0 rArr h = 6

Hence Explained.

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