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(1/2)h-12=-5
We move all terms to the left:
(1/2)h-12-(-5)=0
Domain of the equation: 2)h!=0We add all the numbers together, and all the variables
h!=0/1
h!=0
h∈R
(+1/2)h-12-(-5)=0
We add all the numbers together, and all the variables
(+1/2)h-7=0
We multiply parentheses
h^2-7=0
a = 1; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·1·(-7)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:h_{1}=\frac{-b-\sqrt{\Delta}}{2a}h_{2}=\frac{-b+\sqrt{\Delta}}{2a}
The end solution:
\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*1}=\frac{0-2\sqrt{7}}{2} =-\frac{2\sqrt{7}}{2} =-\sqrt{7}h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*1}=\frac{0+2\sqrt{7}}{2} =\frac{2\sqrt{7}}{2} =\sqrt{7}
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