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X2+5X=22
We move all terms to the left:
X2+5X-(22)=0
We add all the numbers together, and all the variables
X^2+5X-22=0
a = 1; b = 5; c = -22;
Δ = b2-4ac
Δ = 52-4·1·(-22)
Δ = 113
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{113}}{2*1}=\frac{-5-\sqrt{113}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{113}}{2*1}=\frac{-5+\sqrt{113}}{2} $
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