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800=(20+2x)(12+2x)
We move all terms to the left:
800-((20+2x)(12+2x))=0
We add all the numbers together, and all the variables
-((2x+20)(2x+12))+800=0
We multiply parentheses ..
-((+4x^2+24x+40x+240))+800=0
We calculate terms in parentheses: -((+4x^2+24x+40x+240)), so:We get rid of parentheses
(+4x^2+24x+40x+240)
We get rid of parentheses
4x^2+24x+40x+240
We add all the numbers together, and all the variables
4x^2+64x+240
Back to the equation:
-(4x^2+64x+240)
-4x^2-64x-240+800=0
We add all the numbers together, and all the variables
-4x^2-64x+560=0
a = -4; b = -64; c = +560;
Δ = b2-4ac
Δ = -642-4·(-4)·560
Δ = 13056
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13056}=\sqrt{256*51}=\sqrt{256}*\sqrt{51}=16\sqrt{51}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{51}}{2*-4}=\frac{64-16\sqrt{51}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{51}}{2*-4}=\frac{64+16\sqrt{51}}{-8} $
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