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

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

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


m%5E2-6m=16 Start with the given equation


m%5E2-6m-16=0 Subtract 16 from both sides.

%28m-8%29%28m%2B2%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
m-8=0 or m%2B2=0

m=8 or m=-2 Now solve for m in each case


So our answer is
m=8 or m=-2


Notice if we graph y=x%5E2-6x-16 (just replace m with x) we can see that the roots are x=8 and x=-2 . So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+x%5E2-6x-16%29+






# 2


x%5E2%2B5x=3 Start with the given equation


x%5E2%2B5x-3=0 Subtract 3 from both sides.

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


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve x%5E2%2B5%2Ax-3=0 ( notice a=1, b=5, and c=-3)




x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A-3+%29%29%2F%282%2A1%29 Plug in a=1, b=5, and c=-3



x+=+%28-5+%2B-+sqrt%28+25-4%2A1%2A-3+%29%29%2F%282%2A1%29 Square 5 to get 25



x+=+%28-5+%2B-+sqrt%28+25%2B12+%29%29%2F%282%2A1%29 Multiply -4%2A-3%2A1 to get 12



x+=+%28-5+%2B-+sqrt%28+37+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-5+%2B-+sqrt%2837%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-5+%2B-+sqrt%2837%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-5+%2B+sqrt%2837%29%29%2F2 or x+=+%28-5+-+sqrt%2837%29%29%2F2


Now break up the fraction


x=-5%2F2%2Bsqrt%2837%29%2F2 or x=-5%2F2-sqrt%2837%29%2F2




So these expressions approximate to

x=0.54138126514911 or x=-5.54138126514911


So our solutions are:
x=0.54138126514911 or x=-5.54138126514911

Notice when we graph x%5E2%2B5%2Ax-3, we get:



when we use the root finder feature on a calculator, we find that x=0.54138126514911 and x=-5.54138126514911.So this verifies our answer