Im learning factorization and I have to solve for this:
5g to the squared power - 13g + 6 = 0
how should i do it?
5 g^2 -13 g + 6 = 0 (I think you mean)
(5g-3)(g-2) = 0
g = 3/5 or 2
was up
To solve the equation 5g^2 - 13g + 6 = 0, you can use factorization. Here's how you can do it step by step:
Step 1: Make sure the equation is in the form of a quadratic equation, which is in the form ax^2 + bx + c = 0. In this case, we already have it in that form.
Step 2: Identify two numbers that multiply together to give you the product of the coefficient of g^2 (which is 5) multiplied by the constant term (which is 6). In this case, the two numbers are 2 and 3 since 2 * 3 = 6.
Step 3: Rewrite the middle term (-13g) using the two numbers from step 2. Replace -13g with -2g - 11g so that the equation becomes 5g^2 - 2g - 11g + 6 = 0.
Step 4: Group the terms so that the first two terms can be factored and the last two terms can be factored separately. This gives us (5g^2 - 2g) + (-11g + 6) = 0.
Step 5: Factor out the greatest common factor from each group. In the first group, we can factor out g, and in the second group, we can factor out -1. This results in g(5g - 2) - 1(11g - 6) = 0.
Step 6: Now factor out the common term from the equation, which is (5g - 2). This gives us (5g - 2)(g - 1) = 0.
Step 7: Set each factor equal to zero and solve for g. So, either 5g - 2 = 0 or g - 1 = 0.
Step 8: Solve for g in each equation. For 5g - 2 = 0, add 2 to both sides and then divide by 5 which gives g = 2/5. For g - 1 = 0, add 1 to both sides to get g = 1.
Therefore, the solutions to the equation 5g^2 - 13g + 6 = 0 are g = 2/5 and g = 1.