Assuming the equation is:
y = 0.04x^color(red)(2) + 8.3x + 4.3y=0.04x2+8.3x+4.3
The quadratic formula states:
For color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0ax2+bx+c=0, the values of xx 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))x=−b±√b2−(4ac)2⋅a
Substituting:
color(red)(0.04)0.04 for color(red)(a)a
color(blue)(8.3)8.3 for color(blue)(b)b
color(green)(4.3)4.3 for color(green)(c)c gives:
x = (-color(blue)(8.3) +- sqrt(color(blue)(8.3)^2 - (4 * color(red)(0.04) * color(green)(4.3))))/(2 * color(red)(0.04))x=−8.3±√8.32−(4⋅0.04⋅4.3)2⋅0.04
x = (-color(blue)(8.3) +- sqrt(68.89 - 0.688))/0.08x=−8.3±√68.89−0.6880.08
x = (-8.3 +- sqrt(68.202))/0.08x=−8.3±√68.2020.08
If it is necessary to get to a single number:
x = (-8.3 - 8.258)/0.08x=−8.3−8.2580.08 and x = (-8.3 + 8.258)/0.08x=−8.3+8.2580.08
x = -16.558/0.08x=−16.5580.08 and x = -0.042/0.08x=−0.0420.08
x = -206.975x=−206.975 and x = --0.525x=−−0.525
rounded to the nearest thousandth
