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5X^2-2X+2=X2-6X+9
We move all terms to the left:
5X^2-2X+2-(X2-6X+9)=0
We add all the numbers together, and all the variables
5X^2-(+X^2-6X+9)-2X+2=0
We get rid of parentheses
5X^2-X^2+6X-2X-9+2=0
We add all the numbers together, and all the variables
4X^2+4X-7=0
a = 4; b = 4; c = -7;
Δ = b2-4ac
Δ = 42-4·4·(-7)
Δ = 128
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{2}}{2*4}=\frac{-4-8\sqrt{2}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{2}}{2*4}=\frac{-4+8\sqrt{2}}{8} $
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