Solving these Quadratics for x using factoring 2x^2+5x = 3

x = 1/2 ; x = -3

Step-by-step explanation:

To solve this problem, we first need the quadratic to be set equal to x.  Then, we can use factoring to solve for the values of x.

2x^2 + 5x = 3

2x^2 + 5x + -3 = 3 + -3

2x^2 + 5x + -3 = 0

Note that the first term's coefficient is 2.  This factors into 1 and 2.

Note that the third term's coefficient is -3.  This factors into 3 and -1.

From here, we will simply create the binomial factors for the quadratic.

(2x - 1) (x + 3) = 0

2x - 1 = 0  ;  x + 3 = 0

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

2x = 1  ;  x = -3

2x * 1/2 = 1 * 1/2  ;  x = -3

x = 1/2  ;  x = -3

So our solutions for this quadratic equation are x = 1/2 or x = -3.

Cheers.

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