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:

z² + 5z - 12 = -z + 4
z² + 5z - 12 - 4 = -z
z² + 5z + z - 16 = 0
z² + 6z - 16 = 0

Next, factor the quadratic equation:

z² + 6z - 16 = 0
(z - 2)(z + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 2) or (z + 8) must equal zero:

If (z - 2) = 0, z must equal 2
If (z + 8) = 0, z must equal -8

So the solution is that z = 2 or -8

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 4 x 8) + (2 x 8 x 1) + (2 x 4 x 1)
sa = (64) + (16) + (8)
sa = 88

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 1. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 4) and (2, -2) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = -1\(\frac{1}{2}\)x + 1

The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.

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).