Hi Jasmine,

Solving quadratic equation is a big part of Algebra 1 course.

One of the methods is to use Zero Product Property: if a product equal zero then one of the factors should be equal zero. It means that if *a×b=0
*then *a=0 or b=0.*

In order to use Zero Product Property for your equation you need to rewrite left side of the equation in factored form.

Since you are asking about solving quadratic equation you should know how to factor a trinomial. I will refresh your memory anyway. There is a nice 'grouping method' for factoring.

If you have trinomial 2x^{2}+5x-3. First you want to find product of first and third term coefficients: 2×(-3)=-6 Now you need to find two numbers that give you -6 when multiplied and 5 when added. This is like guess and check game. Out of all possible pairs of factors for -6 (-1 and 6, 1 and -6, -2 and 3, 2 and -3) only -1+6=5. Next step is to rewrite 5x as -1x+6x.

2x^{2}+5x-3= 2x^{2}+(-1)x+6x-3

Now use distributive property

2x^{2}+(-1)x+6x-3=x(2x-1)+3(2x-1)

2x-1 is a common factor, so we can use distributive property again

(2x-1)(x+3) a factored form of trinomial 2x^{2}+5x-3

To solve equation 2x^{2}+5x-3=0, we need to solve equation (2x-1)(x+3)=0.

Now we are ready to apply Zero Product Property: if product of (2x-1) and (x+3) equal zero then

2x-1=0 or x+3=0

Inctead of solving one quadratic equation you need to solve two easy equations. Both solutions will be solutions of original equation.

If you follow my steps you can solve your equation by yourself. Good luck.

Olga

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