x2-3x+5=(x+5)2

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Solution for x2-3x+5=(x+5)2 equation:



x2-3x+5=(x+5)2
We move all terms to the left:
x2-3x+5-((x+5)2)=0
We add all the numbers together, and all the variables
x^2-3x-((x+5)2)+5=0
We calculate terms in parentheses: -((x+5)2), so:
(x+5)2
We multiply parentheses
2x+10
Back to the equation:
-(2x+10)
We get rid of parentheses
x^2-3x-2x-10+5=0
We add all the numbers together, and all the variables
x^2-5x-5=0
a = 1; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·1·(-5)
Δ = 45
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:
$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{5}}{2*1}=\frac{5-3\sqrt{5}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{5}}{2*1}=\frac{5+3\sqrt{5}}{2} $

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