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How do you solve 2x^2+3x-2=0

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3 Answers

     2x2 + 3x - 2 = 0 

Here you have a quadratic equation with one unknown variable (x). Since the equation is set equal to 0, we solve for it by factoring the left hand side of the equation and then apply the zero product property to solve for the unknown variable (x). 

Factoring:          2x2 + 3x - 2 = 0

                        (2x - 1)(x + 2) = 0

Zero product property:          (2x - 1)(x + 2) = 0

                                   2x - 1 = 0              AND            x + 2 = 0

          2x - 1 = 0                              AND             x + 2 = 0

             + 1    + 1                                                  - 2     - 2

      ______________                                      _______________

              2x = 1                                                        x = -2

     (2x) / 2 = (1) / 2

              x = 1/2


Thus, the solution to this equation is:       x = 1/2     and     x = -2

Comments

When plotting the solution to a quadratic equation on a graph, these are the two x points, where y is equal to zero and the parabola crosses the x axis.  It is also important to note that if the problem had not been easily factorable, one may have chosen to use the quadratic formula.  If there is no real solution for x, then the parabola does not cross the x axis, if there is one solution then it touches the x axis once (at the vertex) and if there are two solutions it is the same as what was solved for above.

If you get a more difficult polynomial, you can always use the quadratic equation:

x = (-b +/- sqrt(b^2 -4ac))/2a

where you have ax^2 + bx + c

so a=2, b=3, c=-2

x=(-3+/- sqrt(3^2-(4(2)(-2)))/2(2)

x=(-3+/- sqrt(9+16))/4

x=(-3+/-5)/4

x=-8/4=-2  and x=2/4 = 1/2

x= -2 and 1/2

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 2x2+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.

2x2+5x-3= 2x2+(-1)x+6x-3

Now use distributive property 

2x2+(-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 2x2+5x-3

To solve equation 2x2+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