An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

a² - 5a - 59 = -5a + 5
a² - 5a - 59 - 5 = -5a
a² - 5a + 5a - 64 = 0
a² - 64 = 0

Next, factor the quadratic equation:

a² - 64 = 0
(a - 8)(a + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 8) or (a + 8) must equal zero:

If (a - 8) = 0, a must equal 8
If (a + 8) = 0, a must equal -8

So the solution is that a = 8 or -8

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

-5c + 4y = -2c + 9y - 1
-5c = -2c + 9y - 1 - 4y
-5c + 2c = 9y - 1 - 4y
-3c = 5y - 1
c = \( \frac{5y - 1}{-3} \)
c = \( \frac{5y}{-3} \) + \( \frac{-1}{-3} \)
c = -1\(\frac{2}{3}\)y + \(\frac{1}{3}\)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 20° - 26° = 134°

So, d° = 26° + 134° = 160°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 20° = 160°

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.