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10x-(10+x^2)=0
We get rid of parentheses
-x^2+10x-10=0
We add all the numbers together, and all the variables
-1x^2+10x-10=0
a = -1; b = 10; c = -10;
Δ = b2-4ac
Δ = 102-4·(-1)·(-10)
Δ = 60
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{15}}{2*-1}=\frac{-10-2\sqrt{15}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{15}}{2*-1}=\frac{-10+2\sqrt{15}}{-2} $
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