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

-3b + 9z = 3b - 5z + 7
-3b = 3b - 5z + 7 - 9z
-3b - 3b = -5z + 7 - 9z
-6b = -14z + 7
b = \( \frac{-14z + 7}{-6} \)
b = \( \frac{-14z}{-6} \) + \( \frac{7}{-6} \)
b = 2\(\frac{1}{3}\)z - 1\(\frac{1}{6}\)

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 = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

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 = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses.

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.