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1/2x+1/2x+(x-25)+100-15=540
We move all terms to the left:
1/2x+1/2x+(x-25)+100-15-(540)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
1/2x+1/2x+(x-25)-455=0
We get rid of parentheses
1/2x+1/2x+x-25-455=0
We multiply all the terms by the denominator
x*2x-25*2x-455*2x+1+1=0
We add all the numbers together, and all the variables
x*2x-25*2x-455*2x+2=0
Wy multiply elements
2x^2-50x-910x+2=0
We add all the numbers together, and all the variables
2x^2-960x+2=0
a = 2; b = -960; c = +2;
Δ = b2-4ac
Δ = -9602-4·2·2
Δ = 921584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{921584}=\sqrt{16*57599}=\sqrt{16}*\sqrt{57599}=4\sqrt{57599}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-960)-4\sqrt{57599}}{2*2}=\frac{960-4\sqrt{57599}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-960)+4\sqrt{57599}}{2*2}=\frac{960+4\sqrt{57599}}{4} $
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