SOLUTION: Please take this equation and solve by factoring, completing the square and quadratic equation. Then leave an equation for your classmates to try. x² + 2x -8=0

To solve by factoring, the easiest way when it works:



Use the zero factor problem, by setting each factor = 0



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To solve by completing the square, the hardest way but it always works.



Isolate the terms in x on the left by adding +8 to both sides:



Multiply the coefficient of x, which is 2, by , getting 1, then
square 1, getting .  Add  to each side:



Factor the left side as the product of two identical binomials. Combine
the numbers on the right:



Write the product of two identical binomials as a perfect square:



Use the principle of square roots:



Since the square root of 9 is 3 we have:



We make two equations, one using the + and the other using the -



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To solve by using the quadratic formula: (the medium hard way that
always works):



There is a 1 coefficient understood before the first term:

 

Compare that to 



and find that , , 

Then substitute those three values in

 

 

 

 

 

We make two equations, one using the + and the other using the -



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To make an equation for your classmates to try

Choose two arbitrary numbers of x to be the solutions of the
equation that you're making up.  Let's pick, say -3 and 7

Then reverse the steps in solving by factoring.

Going backward from the zero factor principle:





Going backward from factoring by multiplying this out using FOIL:





That's an equation for your classmates to try.

Edwin