Start by identifying the values of a, b, and c. Be sure that all of the terms of are on the same side and in the correct order for the standard form of a quadratic function.
2 and 3
Practice makes perfect
To solve the given equation by factoring, we will start by identifying the values of a, b, and c.
5x^2-25x=-30 ⇔ 5x^2 - 25x+ 30=0
Notice that we can factor 5 from all three terms as it is the greatest common factor of our expression.
Now we have a quadratic equation with a= 1, b= -5, and c= 6. To factor the left-hand side, we need to find a factor pair of 1 * 6=6 whose sum is -5. Since 6 is a positive number, we will only consider factors with the same sign — both positive or both negative — so that their product is positive.
Factor Pair
Product of Factors
Sum of Factors
1 and 6
1* 6 6
1+6 7
-1 and -6
-1* (-6) 6
-1+(-6) -7
2 and 3
2* 3 6
2+3 5
-2 and -3
-2* (-3) 6
-2+(-3) -5
The integers whose product is 6 and whose sum is - 5 are -2 and -3. With this information, we can rewrite the linear factor on the left-hand side of the equation and factor by grouping.
We found that the solutions to the given equation are x=2 and x=3. To check our answer, we will graph the related functions y=5x^2-25x+30 and y=5(x-2)(x-3) in the same coordinate plane using a graphing calculator.
We see that only one graph appears. This means that both graphs coincide. We can see that the x-intercepts are 2 and 3. Therefore, our solutions are correct. âś“
