-10x^2 + 7x - 1 = 0
Use factoring to solve
(-5x+1)(2x-1) = 0
Check that.
Set each factor to zero and solve for x.
To solve the quadratic equation -10x^2 + 7x - 1 = 0 using factoring, we need to find two binomials whose product is equal to the quadratic expression.
First, let's rearrange the equation in standard form: -10x^2 + 7x - 1 = 0
To factor, we need to find two numbers that multiply to give us the product of -10 times -1, which is 10, and add up to give us the coefficient of the middle term, which is 7.
Looking at the factors of 10, we have (1, 10) and (2, 5). Let's check if any combination of these factors satisfies the second condition.
(1, 10): 1 + 10 = 11 (not 7)
(2, 5): 2 + 5 = 7
So, the factors we need are 2 and 5. Now, we can rewrite the middle term using these two factors:
-10x^2 + 2x + 5x - 1 = 0
Next, we can group the terms:
(-10x^2 + 2x) + (5x - 1) = 0
Now, we can factor out the greatest common factor from each group:
2x(-5x + 1) + 1(5x - 1) = 0
Notice that we now have a common binomial factor, -5x + 1. Let's factor it out:
(2x + 1)(-5x + 1) = 0
Now, we can solve for x by setting each factor equal to zero and solving the resulting equations:
2x + 1 = 0 or -5x + 1 = 0
Solving the first equation, we get:
2x = -1
x = -1/2
Solving the second equation, we get:
-5x = -1
x = 1/5
Hence, the solutions to the quadratic equation -10x^2 + 7x - 1 = 0, obtained by factoring, are x = -1/2 and x = 1/5.