The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

y² - 6y + 5 = 0
(y - 1)(y - 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 1) or (y - 5) must equal zero:

If (y - 1) = 0, y must equal 1
If (y - 5) = 0, y must equal 5

So the solution is that y = 1 or 5

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(1²) + 2π(1 x 7)
sa = 2π(1) + 2π(7)
sa = (2 x 1)π + (2 x 7)π
sa = 2π + 14π
sa = 16π

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

-a - 8y = a + 4y + 4
-a = a + 4y + 4 + 8y
-a - a = 4y + 4 + 8y
-2a = 12y + 4
a = \( \frac{12y + 4}{-2} \)
a = \( \frac{12y}{-2} \) + \( \frac{4}{-2} \)
a = -6y - 2