Solving By Factoring
6x^2-13x=-6
(x-8)(x-5)=x
4x(x-6)-x(x-2)=-24
Please show work I want to learn!!!!!!
You always want to set things equal to zero:
6x^2-13x+6 = 0
Now, just have to have some practice factoring to get to
(3x-2)(2x-3) = 0
Now, since if the product of two numbers is zero, one of the numbers must be zero. So, either
3x-2 = 0 and x = 2/3
or
2x-3 = 0 and x = 3/2
You can always use the quadratic formula, as well, even if it does not factor at all.
6 x^2 - 13 x + 6 = 0
we want 6 * 2 and a 1 to get 13
or 9 and 4
(3 x - 2)( 2x - 3 ) ah, 9 and 4
x = 2/3 or 3/2
4x(x-6)-x(x-2)=-24
4 x^2 - 24 x - x^2 + 2 x + 24 = 0
3 x^2 -22 x + 24 = 0
18 and 4 I bet
(3x - 4)(x - 6) ??? yes
x = 4/3 or 6
Sure! I'll explain how to solve each of these equations by factoring step-by-step.
1) 6x^2 - 13x = -6
To solve this equation, we need to set it equal to zero. So let's rearrange the terms:
6x^2 - 13x + 6 = 0
Now, we can try to factor this quadratic expression. We're looking for two binomials that multiply together to give us the original expression. In this case, we're looking for two numbers whose product is (6 * 6) = 36, and whose sum is -13.
After some trial and error, we see that -4 and -9 are the numbers we're looking for.
So, we can factor the expression as:
(2x - 3)(3x - 2) = 0
Now we can set each factor equal to zero and solve for x:
2x - 3 = 0 (or) 3x - 2 = 0
Solving these equations, we find:
2x = 3 (or) 3x = 2
x = 3/2 (or) x = 2/3
Thus, the solution to the equation is x = 3/2 or x = 2/3.
2) (x-8)(x-5) = x
We expand the left side of the equation by using the distributive property:
x^2 - 5x - 8x + 40 = x
x^2 - 13x + 40 - x = 0
Combining like terms, we get:
x^2 - 14x + 40 = 0
Now, we'll try to factor this quadratic expression:
We're looking for two numbers that multiply together to give us (1 * 40) = 40 and whose sum is -14.
After some trial and error, we find that -10 and -4 are the numbers we need.
So we can factor the expression as:
(x - 10)(x - 4) = 0
Setting each factor equal to zero and solving for x:
x - 10 = 0 (or) x - 4 = 0
Solving these equations, we find:
x = 10 (or) x = 4
Thus, the solution to the equation is x = 10 or x = 4.
3) 4x(x-6) - x(x-2) = -24
We'll start expanding both sides of the equation by using the distributive property:
4x^2 - 24x - x^2 + 2x = -24
Combining like terms, we get:
3x^2 - 22x = -24
Now, let's move all terms to the left side of the equation:
3x^2 - 22x + 24 = 0
Now, we'll try to factor this quadratic expression:
We're looking for two numbers that multiply together to give us (3 * 24) = 72 and whose sum is -22.
After some trial and error, we find that -6 and -18 are the numbers we need.
We can now factor the expression as:
(x - 6)(3x - 4) = 0
Setting each factor equal to zero and solving for x:
x - 6 = 0 (or) 3x - 4 = 0
Solving these equations, we find:
x = 6 (or) 3x = 4
x = 6 (or) x = 4/3
Thus, the solution to the equation is x = 6 or x = 4/3.
I hope that helps! Let me know if you have any other questions.