How Do You Solve H^2=-3h+54? - Socratic

How do you solve #h^2=-3h+54#? Algebra Quadratic Equations and Functions Comparing Methods for Solving Quadratics

3 Answers

Mark D. Mar 30, 2018

#h =-9 or h = 6#

Explanation:

Rearrange to get

#h^2 + 3h - 54 = 0#

Factorise

#( h+ 9)(h - 6) = 0#

#h + 9 = 0 or h- 6 = 0#

#h = - 9 or h =6#

Answer link Jim G. Mar 30, 2018

#h=-9" or "h=6#

Explanation:

#"arrange the equation in standard form"#

#rArrh^2+3h-54=0larrcolor(blue)"in standard form"#

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

#rArr(h+9)(h-6)=0#

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

#h+9=0rArrh=-9#

#h-6=0rArrh=6#

Answer link Soumalya Pramanik Mar 30, 2018

#h = -9, 6#.

Explanation:

We have,

#color(white)(xxx)h^2 = -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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