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

x² + 9x + 14 = 0
(x + 2)(x + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 2) or (x + 7) must equal zero:

If (x + 2) = 0, x must equal -2
If (x + 7) = 0, x must equal -7

So the solution is that x = -2 or -7

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 38° - 36° = 106°

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(3a)(3ab) + (7a²)(8b)
(3 x 3)(a x a x b) + (7 x 8)(a² x b)
(9)(a¹⁺¹ x b) + (56)(a²b)
9a²b + 56a²b
65a²b

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -12 as well and sum (Inside, Outside) to equal -1. For this problem, those two numbers are -4 and 3. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - y - 12
y² + (-4 + 3)y + (-4 x 3)
(y - 4)(y + 3)

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with c° = 14, the value of w° is 14.