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
