How do you solve #x^2 + 8x=0# using the quadratic formula?

1 Answer
Aug 28, 2017

Answer:

See a solution process below:

Explanation:

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#