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(10x+525)(10x+509)=134
We move all terms to the left:
(10x+525)(10x+509)-(134)=0
We multiply parentheses ..
(+100x^2+5090x+5250x+267225)-134=0
We get rid of parentheses
100x^2+5090x+5250x+267225-134=0
We add all the numbers together, and all the variables
100x^2+10340x+267091=0
a = 100; b = 10340; c = +267091;
Δ = b2-4ac
Δ = 103402-4·100·267091
Δ = 79200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{79200}=\sqrt{3600*22}=\sqrt{3600}*\sqrt{22}=60\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10340)-60\sqrt{22}}{2*100}=\frac{-10340-60\sqrt{22}}{200} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10340)+60\sqrt{22}}{2*100}=\frac{-10340+60\sqrt{22}}{200} $
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