# How to solve this? 0.01 x^2 - 0.1 x - 0.3 = 0

hala718 | High School Teacher | (Level 1) Educator Emeritus

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0.01 x^2 -0.1 x -0.3 =0

First let us multiply by 100 so x^2 factor is 1

x^2 -10x -30=0

x1= [10+sqrt(100+120)]/2

=  5+sqrt(55)

x2 = [10- sqrt(220)]/2

= 5-sqrt(55)

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Let's write the coefficients as quotients, like:

(1/100)*x^2 - (1/10)*x - 3/10 = 0

Thecommon denominator of quotients is 100, so we'll multiply the second and the third quotient by 10.

The equation will become:

x^2 - 10x - 30 = 0

x1 = [10 + sqrt(100+120)]/2

x1 = (10+2sqrt55)/2

We'll factorize and we'll divide by 2:

x1 = 5+sqrt55

x2 = 5-sqrt55

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve:

0.01 x^2 - 0.1 x - 0.3 = 0

Solution:

The numerical coeficients are in fractions. So we could do away with this by the LCM of denominators of 1/100,1/10 and 3/10, that is, 100:

100*01x^2-100*01x-100*0.3 = 0. Or

x^2-10x-30 = 0. Or

x^2 -10x +5^2 - 5^2 -30 = 0. Or

(x-5)^2  = 55. Or

x-5 = +or- (sqrt55) Or

x = 5+sqrt55 or x = 5-sqrt55