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(42+x)x=400
We move all terms to the left:
(42+x)x-(400)=0
We add all the numbers together, and all the variables
(x+42)x-400=0
We multiply parentheses
x^2+42x-400=0
a = 1; b = 42; c = -400;
Δ = b2-4ac
Δ = 422-4·1·(-400)
Δ = 3364
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{3364}=58$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-58}{2*1}=\frac{-100}{2} =-50 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+58}{2*1}=\frac{16}{2} =8 $
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