Solve the equation by factoring.
2x^2 + 8x + 1 = 0
How do I arrive at this answer?
-2 + or - radical 14 over 2
First of all the equation does not factor over the rationals.
Secondly your answer is not correct.
use the formula
x = (-8 ±√(64-4(2)(1))/4
= (-8 ±√56)/4
= (-8 ± 2√14)/4
= (-4 ± √14)/2
(it works, I subbed it back in)
the answer i provided was from the back of the book.
To solve the quadratic equation 2x^2 + 8x + 1 = 0 by factoring, you need to find two binomials that multiply together to give you the quadratic expression.
Step 1: Write down the equation in the standard form ax^2 + bx + c = 0, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = 8, and c = 1.
Step 2: Look for two numbers that multiply to give you a product of ac (the product of the coefficient of x^2 and the constant term). In this case, ac = (2)(1) = 2.
The numbers that multiply to give 2 are 1 and 2, or -1 and -2.
Step 3: Rewrite the middle term (bx) using the two numbers you found in step 2. To do this, split the middle term into two terms using these numbers. In this case, the middle term is 8x, and the two numbers that multiply to give 2 are 1 and 2. So, rewrite 8x as 2x + 6x.
The equation becomes 2x^2 + 2x + 6x + 1 = 0.
Step 4: Group the terms and factor by grouping. Group the first two terms and the last two terms separately.
(2x^2 + 2x) + (6x + 1) = 0.
Step 5: Factor out the greatest common factor from each group.
2x(x + 1) + 1(6x + 1) = 0.
Step 6: Combine the factored terms.
2x(x + 1) + 1(6x + 1) = 0.
Step 7: Apply the zero-product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. Set each factor equal to zero and solve for x.
2x = 0 --> x = 0.
x + 1 = 0 --> x = -1.
6x + 1 = 0 --> 6x = -1 --> x = -1/6.
Step 8: Write down the solutions.
x = 0, -1, -1/6.
Therefore, the solutions to the equation 2x^2 + 8x + 1 = 0 are x = 0, x = -1, and x = -1/6.