First, put the equation in standard form:
#g^2 + g = 56#
#g^2 + g - color(red)(56) = 56 - color(red)(56)#
#g^2 + g - 56 = 0#
Next, factor the left side of the equation as:
#(g + 8)(g - 7) = 0#
Now, solve each term on the left for #0# to find the solutions:
Solution 1:
#g + 8 = 0#
#g + 8 - color(red)(8) = 0 - color(red)(8)#
#g + 0 = -8#
#g = -8#
Solution 2:
#g - 7 = 0#
#g - 7 + color(red)(7) = 0 + color(red)(7)#
#g - 0 = 7#
#g = 7#
The Solution Is:
#g = {-8, 7}#
Another process is to use the quadratic formula:
The quadratic formula states:
For #color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0#, the values of #x# which are the solutions to the equation are given by:
#x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))#
Substituting:
#color(red)(1)# for #color(red)(a)#
#color(blue)(1)# for #color(blue)(b)#
#color(green)(-56)# for #color(green)(c)# gives:
#g = (-color(blue)(1) +- sqrt(color(blue)(1)^2 - (4 * color(red)(1) * color(green)(-56))))/(2 * color(red)(1))#
#g = (-1 +- sqrt(1 - (-224)))/2#
#g = (-1 +- sqrt(1 + 224))/2#
#g = (-1 +- sqrt(225))/2#
#g = (-1 - sqrt(225))/2# or #g = (-1 + sqrt(225))/2#
#g = (-1 - 15)/2# or #g = (-1 + 15)/2#
#g = (-16)/2# or #g = 14/2#
#g = -8# or #g = 7#
#g = {-8, 7}#
