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x(x+5)+2x+1=30
We move all terms to the left:
x(x+5)+2x+1-(30)=0
We add all the numbers together, and all the variables
2x+x(x+5)-29=0
We multiply parentheses
x^2+2x+5x-29=0
We add all the numbers together, and all the variables
x^2+7x-29=0
a = 1; b = 7; c = -29;
Δ = b2-4ac
Δ = 72-4·1·(-29)
Δ = 165
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{-(7)-\sqrt{165}}{2*1}=\frac{-7-\sqrt{165}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{165}}{2*1}=\frac{-7+\sqrt{165}}{2} $
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