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2x-5-18x=(-1/2)(22x+10)
We move all terms to the left:
2x-5-18x-((-1/2)(22x+10))=0
Domain of the equation: 2)(22x+10))!=0We add all the numbers together, and all the variables
x∈R
-16x-((-1/2)(22x+10))-5=0
We multiply parentheses ..
-((-22x^2-1/2*10))-16x-5=0
We multiply all the terms by the denominator
-((-22x^2-1-16x*2*10))-5*2*10))=0
We calculate terms in parentheses: -((-22x^2-1-16x*2*10)), so:We add all the numbers together, and all the variables
(-22x^2-1-16x*2*10)
We get rid of parentheses
-22x^2-16x*2*10-1
Wy multiply elements
-22x^2-320x*1-1
Wy multiply elements
-22x^2-320x-1
Back to the equation:
-(-22x^2-320x-1)
-(-22x^2-320x-1)=0
We get rid of parentheses
22x^2+320x+1=0
a = 22; b = 320; c = +1;
Δ = b2-4ac
Δ = 3202-4·22·1
Δ = 102312
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{102312}=\sqrt{1764*58}=\sqrt{1764}*\sqrt{58}=42\sqrt{58}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-42\sqrt{58}}{2*22}=\frac{-320-42\sqrt{58}}{44} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+42\sqrt{58}}{2*22}=\frac{-320+42\sqrt{58}}{44} $
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