How do you solve quadratics by taking square roots ?

Start with the equation

Factor from the first two terms:

Complete the square; do this by adding an appropriate constant to to form a perfect square trinomial. Recall that

So here we have

and we have to add to make the perfect square. But we also have to subtract this same constant to preserve equality:

Now we can take the square root and solve for :

You should recognize this formula...

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629