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Suppose a classmate missed the lessons on completing the square to find the center and radius of a circle. Explain the process to that classmate. If it helps, use a problem you’ve already done, as an example.
Match each expression with the value needed in the box in order for the expression to be a perfect square trinomial.
\(x^2-8x+\boxed{\phantom{3}}\)
\(x^2+20x+\boxed{\phantom{3}}\)
\(x^2-16x+\boxed{\phantom{3}}\)
\(x^2+9x+\boxed{\phantom{3}}\)
16
20.25
64
100
Find the center and radius of the circle represented by the equation \(x^2+y^2+4x-10y+20=0\).
Find the solution or solutions to each equation.
Mai is using the quadratic formula to solve two different quadratic equations.
For the first equation, she writes \(x= \dfrac{\text-4 \pm \sqrt{4^2 - 4(4)(1)}}{2(4)}\).
For the second equation, she writes \(x=\dfrac{3 \pm \sqrt{(\text-3)^2 - 4(3)(5)}}{2(3)}\).
How many real solutions will each equation have? Explain how you know.