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 area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 8 x 3 = \( \frac{24}{2} \) = 12

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(4 + 3)(3)
a = ½(7)(3)
a = ½(21) = \( \frac{21}{2} \)
a = 10\(\frac{1}{2}\)

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 + 7a - 10 = 3a - 5
a² + 7a - 10 + 5 = 3a
a² + 7a - 3a - 5 = 0
a² + 4a - 5 = 0

Next, factor the quadratic equation:

a² + 4a - 5 = 0
(a - 1)(a + 5) = 0

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

If (a - 1) = 0, a must equal 1
If (a + 5) = 0, a must equal -5

So the solution is that a = 1 or -5