Solve: 4x ^ 2 – 5x – 12 = 0

To solve the quadratic equation 4x^2 – 5x – 12 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 – 4ac)) / (2a)

For the given equation, a = 4, b = -5, and c = -12. Plugging in these values into the quadratic formula, we have:

x = (-(-5) ± √((-5)^2 – 4 * 4 * -12)) / (2 * 4) = (5 ± √(25 + 192)) / 8 = (5 ± √217) / 8

Therefore, the solutions to the equation 4x^2 – 5x – 12 = 0 are:

x = (5 + √217) / 8 x = (5 – √217) / 8

Solve: x + 9 = 18 + -2x

To solve the equation x + 9 = 18 + -2x, we can start by simplifying both sides of the equation.

First, let’s remove the parentheses by distributing the -2 to both terms in the expression 18 + -2x:

x + 9 = 18 – 2x

Next, let’s combine like terms by moving all the x terms to one side of the equation and the constant terms to the other side:

x + 2x = 18 – 9

This simplifies to:

3x = 9

To solve for x, we divide both sides of the equation by 3:

(3x)/3 = 9/3

This gives us:

x = 3

Therefore, the solution to the equation x + 9 = 18 + -2x is x = 3.