SOLUTION: Solve. 1) m squared - 6m = 16 2) x squared + 5x = 3

Question 124652: Solve.
1) m squared - 6m = 16

2) x squared + 5x = 3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Start with the given equation

Subtract 16 from both sides.

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for m in each case

So our answer is
or

Notice if we graph (just replace m with x) we can see that the roots are and . So this visually verifies our answer.

# 2

Start with the given equation

Subtract 3 from both sides.

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=5, and c=-3

Square 5 to get 25

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Now break up the fraction

or

So these expressions approximate to

or

So our solutions are:
or

Notice when we graph , we get:

when we use the root finder feature on a calculator, we find that and .So this verifies our answer

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