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10x^2+2=283
We move all terms to the left:
10x^2+2-(283)=0
We add all the numbers together, and all the variables
10x^2-281=0
a = 10; b = 0; c = -281;
Δ = b2-4ac
Δ = 02-4·10·(-281)
Δ = 11240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11240}=\sqrt{4*2810}=\sqrt{4}*\sqrt{2810}=2\sqrt{2810}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2810}}{2*10}=\frac{0-2\sqrt{2810}}{20} =-\frac{2\sqrt{2810}}{20} =-\frac{\sqrt{2810}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2810}}{2*10}=\frac{0+2\sqrt{2810}}{20} =\frac{2\sqrt{2810}}{20} =\frac{\sqrt{2810}}{10} $
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