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 > sign and the answer on the other.

-2a + 1 > -8 - 3a
-2a > -8 - 3a - 1
-2a + 3a > -8 - 1
a > -9

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

x² + 5x - 6 = 0
(x - 1)(x + 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 1) or (x + 6) must equal zero:

If (x - 1) = 0, x must equal 1
If (x + 6) = 0, x must equal -6

So the solution is that x = 1 or -6

To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

The area of a parallelogram is equal to its length x width:

a = l x w
a = a x b
a = 6 x 1
a = 6

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)