SOLUTION: I tried to start this problem by putting it in standard form but I'm stuck from here X^2=10x-24 X^2-10x+24=0 a=X, b=-10, c=24 How do I solve for the root

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Question 66057This question is from textbook beginning algebra
: I tried to start this problem by putting it in standard form but I'm stuck from here
X^2=10x-24
X^2-10x+24=0
a=X, b=-10, c=24
How do I solve for the rootThis question is from textbook beginning algebra

Answer by algebrapro18(206) About Me  (Show Source):
You can put this solution on YOUR website!
Well to solve a quadratic equation by factoring you need to do the following:

1)Factor the quadratic equation
a)Multiply the a and c terms together where a and c are coefficients.
b)Factor that number and see what factors add to the b term.
*Note: You might end up haveing to take the negative of both factors to get
them to add right.
c)re-write the equation as a product of its factors.
2)Set each factor equal to 0 and solve

X^2-10x+24=0

a = 1, b = -10, c = 24

a*c = 1* 24 = 24

Factors of 24 are:
1 and 24
2 and 12
3 and 8
4 and 6

-4 * -6 = 24
-4 + -6 = 10

X^2-10x+24=0
=> (x-4)(x-6) = 0

now solve each equation for 0
x - 4 = 0
x = 4

x - 6 = 0
x = 6

so your roots are x = 6 and x = 4 now check your work.

4^2-10(4)+24=0
16-40+24=0
0=0 therefor x = 4 is a right answer

6^2-10(6)+24=0
36-60+24=0
0=0 therefor x = 6 is a right answer and we are done.