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(1/2)4x=180
We move all terms to the left:
(1/2)4x-(180)=0
Domain of the equation: 2)4x!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+1/2)4x-180=0
We multiply parentheses
4x^2-180=0
a = 4; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·4·(-180)
Δ = 2880
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*4}=\frac{0-24\sqrt{5}}{8} =-\frac{24\sqrt{5}}{8} =-3\sqrt{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*4}=\frac{0+24\sqrt{5}}{8} =\frac{24\sqrt{5}}{8} =3\sqrt{5} $
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