SOLUTION: 1. x^2+6x-5=0 2. 4x^2 + 20x = 0 3. 3x^2 + 10x + 8 = -17x - 2 4. x^2 + 3x - 40 = 0 5. p^2 + 15p + 25 = 6p + 5 6. x^2 = 10x - 24

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#1

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=6, and c=-5



Square 6 to get 36



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


Simplify


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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#2


Start with the given equation

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 x in each case


So our answer is
or


Notice if we graph we can see that the roots are and . So this visually verifies our answer.