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(1/2)(2x)(x)=196
We move all terms to the left:
(1/2)(2x)(x)-(196)=0
Domain of the equation: 2)2xx!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+1/2)2xx-196=0
We multiply parentheses
2x^2-196=0
a = 2; b = 0; c = -196;
Δ = b2-4ac
Δ = 02-4·2·(-196)
Δ = 1568
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{2}}{2*2}=\frac{0-28\sqrt{2}}{4} =-\frac{28\sqrt{2}}{4} =-7\sqrt{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{2}}{2*2}=\frac{0+28\sqrt{2}}{4} =\frac{28\sqrt{2}}{4} =7\sqrt{2} $
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