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X2+7X-44=9
We move all terms to the left:
X2+7X-44-(9)=0
We add all the numbers together, and all the variables
X^2+7X-53=0
a = 1; b = 7; c = -53;
Δ = b2-4ac
Δ = 72-4·1·(-53)
Δ = 261
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{29}}{2*1}=\frac{-7-3\sqrt{29}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{29}}{2*1}=\frac{-7+3\sqrt{29}}{2} $
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