Question

Solve the equation 4x² + 4x - 9 = 0 and round
the roots to the nearest hundredth.

Answer 1

x = 1.08 and x = -2.08

Explanation:

We can solve this equation using the quadratic formula.

• In order to understand the quadratic formula, we must first realize that the equation is currently in standard form and the general formula for the standard form of a quadratic equation is

`ax^2+bx+c=0`

• We must also remember that the quadratic formula can have two solutions since you can have a positive square (e.g., 4 * 4 = 16) and a negative square (e.g., -4 * -4 = 16)

Thus, in the equation given, 4 is our a value, 4 is (also) our b value and -9 is our c value.

The formula for the positive solution of the quadratic formula is

`x=(-b+√(b^2-4ac) )/(2a)`

The formula for the negative solution of the quadratic formula is

`x=(-b-√(b^2-4ac) )/(2a)`

Positive solution:

`x=(-4+√(4^2-4(4)(-9)) )/(2(4))\\ \\x=(-4+√(160) )/(8)\\ \\x=1.08113883\\\\x=1.08`

Negative solution:

`x=(-4-√(4^2-4(4)(-9)) )/(2(4))\\ \\x=(-4-√(160) )/(8)\\ \\x=-2.08113883\\\\x=-2.08`