For the given quadratic equation lesser x=3.765 and greater x=8.235.
The given quadratic equation is (x-6)²-5=0.
We need to find the solutions from least to greatest.
What is the formula to find the solution to the quadratic equation?
The formula to find the solution to the quadratic equation is [tex]x=\frac{-b\pm\sqrt{b^{2}-4ac }}{2a}[/tex].
Now, (x-6)²-5=0 can be written as x²-12x+31=0
Here, a=1, b=-12 and c=31
x=(12±√20)/2
⇒x=(12±4.47)/2
⇒x=3.765 or x=8.235
Therefore, lesser x=3.765 and greater x=8.235.
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