x2=4.5

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Solution for x2=4.5 equation:



x2=4.5
We move all terms to the left:
x2-(4.5)=0
We add all the numbers together, and all the variables
x^2-4.5=0
a = 1; b = 0; c = -4.5;
Δ = b2-4ac
Δ = 02-4·1·(-4.5)
Δ = 18
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:
$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{2}}{2*1}=\frac{0-3\sqrt{2}}{2} =-\frac{3\sqrt{2}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{2}}{2*1}=\frac{0+3\sqrt{2}}{2} =\frac{3\sqrt{2}}{2} $

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