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

z² + 4z + 3 = 0
(z + 1)(z + 3) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 1) or (z + 3) must equal zero:

If (z + 1) = 0, z must equal -1
If (z + 3) = 0, z must equal -3

So the solution is that z = -1 or -3

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

9a + 2a = 11a

To solve this equation, 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.

8x - 5 = -7 + 4x
8x = -7 + 4x + 5
8x - 4x = -7 + 5
4x = -2
x = \( \frac{-2}{4} \)
x = -\(\frac{1}{2}\)

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 w° = 39, the value of y° is 141.