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(0.100-x)(0.100-x)=1600x^2
We move all terms to the left:
(0.100-x)(0.100-x)-(1600x^2)=0
determiningTheFunctionDomain -1600x^2+(0.100-x)(0.100-x)=0
We add all the numbers together, and all the variables
-1600x^2+(-1x+0.1)(-1x+0.1)=0
We multiply parentheses ..
-1600x^2+(+x^2-0.1x-0.1x+0.01)=0
We get rid of parentheses
-1600x^2+x^2-0.1x-0.1x+0.01=0
We add all the numbers together, and all the variables
-1599x^2-0.2x+0.01=0
a = -1599; b = -0.2; c = +0.01;
Δ = b2-4ac
Δ = -0.22-4·(-1599)·0.01
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{64}=8$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.2)-8}{2*-1599}=\frac{-7.8}{-3198} =4.3333333333333/1776.6666666667 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+8}{2*-1599}=\frac{8.2}{-3198} =-3.7272727272727/1453.6363636364 $
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