We can rewrite the equation in standard form as:
#x^2 + 8x + 0 = 0#
Now, we can use the quadratic equation to solve this problem:
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)(8)# for #color(blue)(b)#
#color(green)(0)# for #color(green)(c)# gives:
#x = (-color(blue)(8) +- sqrt(color(blue)(8)^2 - (4 * color(red)(1) * color(green)(0))))/(2 * color(red)(1))#
#x = (-color(blue)(8) +- sqrt(64 - 0))/2#
#x = (-color(blue)(8) +- sqrt(64))/2#
#x = (-color(blue)(8) - 8)/2# and #x = (-color(blue)(8) + 8)/2#
#x = -16/2# and #x = 0/2#
#x = -8# and #x = 0#
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A simple way to solve this equation without the quadratic is to factor an #x# out of each term on the left side of the equation:
#x(x + 8) = 0#
Then solve each term on the left for #0#:
Solution 1:
#x = 0#
Solution 2:
#x + 8 = 0#
#x + 8 - color(red)(8) = 0 - color(red)(8)#
#x + 0 = -8#
#x = -8#
