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

x² + 2x - 35 = 0
(x - 5)(x + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 5) or (x + 7) must equal zero:

If (x - 5) = 0, x must equal 5
If (x + 7) = 0, x must equal -7

So the solution is that x = 5 or -7

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.

3z - 9 = 3 - 4z
3z = 3 - 4z + 9
3z + 4z = 3 + 9
7z = 12
z = \( \frac{12}{7} \)
z = 1\(\frac{5}{7}\)

A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

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.

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).