kjones said:
Solve using quadratic formula:
4x^2 + 8x - 16 = 0
Whether you are going to solve a quadratic equation by factoring, completing the square, or by the quadratic formula, smaller numbers are generally easier to work with than larger numbers.
Note that each term in your equation is evenly divisible by 4. So, let's divide both sides of the equation by 4:
x<sup>2</sup> + 2x - 4 = 0
Now, you can use the quadratic formula with
a = 1, b = 2, and c = -4
Substitute these values into the formula:
x = [-2 +/- √(2<sup>2</sup> - 4(1)(-4))] / 2(1)
BE VERY CAREFUL when doing the computation of the quantity under the radical sign. That is where most mistakes occur when using the quadratic formula. I'll walk you through it in baby steps:
(2<sup>2</sup> - 4(1)(-4))
Remember the order of operations. Do the power first:
(4 - 4(1)(-4))
Next, do the multiplications:
(4 - (-16))
Finally, do the subtraction. Remember that 4 - (-16) is the same thing as 4 + 16:
4 + 16
20
So, the expression under the radical sign is 20, and we continue:
x = [-2 +/- √20 ] / 2
We can simplify √20......it is 2 √5. Now we have this:
x = [-2 +/- 2 √5] / 2
or,
x = 2[-1 +/- √5] / 2
or,
x = -1 +/- √5