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x^2-18x+81x=49
We move all terms to the left:
x^2-18x+81x-(49)=0
We add all the numbers together, and all the variables
x^2+63x-49=0
a = 1; b = 63; c = -49;
Δ = b2-4ac
Δ = 632-4·1·(-49)
Δ = 4165
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4165}=\sqrt{49*85}=\sqrt{49}*\sqrt{85}=7\sqrt{85}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-7\sqrt{85}}{2*1}=\frac{-63-7\sqrt{85}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+7\sqrt{85}}{2*1}=\frac{-63+7\sqrt{85}}{2} $
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