Solve by factoring: 2x^2+7x-4=0
(2x-1)(x+4) = 0
etc
Can you explain how to do this one?
Its the same, just a little different setup.
4x^2+10x=x^2-x+4
combine like terms
3x^2 + 11x - 4 = 0
(3x-1)(x+4) = 0
etc
can you show me how to solve the factored equation?
based on the fact that if a multiplication has an answer of zero then one or more of its factors must have been zero, so if
(3x-1)(x+4) = 0
then 3x-1 = 0 or x+4 = 9
3x = 1 or x = -4
x = 1/3 or x = -4
(set each of the factors equal to zero and solve, separate your statements with OR )
Where did the 9 come from in x+4=9?
If you understood the concept you should have figured out that I meant 0 instead of 9
(the 0 is beside the 9 on the keyboard !)
OHHHH. Wow. Haha, sorry, you definitely threw me off with that one. I get it now. Thanks.
solve
42x^2-14x-56=0
To solve the quadratic equation 2x^2 + 7x - 4 = 0 by factoring, we need to find two binomials that multiply together to give us the quadratic expression.
The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constant coefficients. In this case, a = 2, b = 7, and c = -4.
To factor the quadratic equation, we need to find two numbers, let's call them m and n, such that:
1. Their product is equal to the product of the coefficient of x^2 and the constant term, which is a * c.
2. Their sum is equal to the coefficient of x, which is b.
For 2x^2 + 7x - 4 = 0, the product of a * c is 2 * (-4) = -8.
Now we need to find two numbers whose product is -8 and whose sum is 7.
One pair of numbers that satisfies these conditions is 8 and -1. Their product is -8 and their sum is 8 + (-1) = 7.
Using these values, we can rewrite the middle term as the sum of 8x and -x:
2x^2 + 8x -x - 4 = 0
Next, we group the terms into two pairs:
(2x^2 + 8x) + (-x - 4) = 0
Now, we factor out the greatest common factor from each pair:
2x(x + 4) - 1(x + 4) = 0
Notice that we have a common binomial factor of (x + 4). Factoring out (x + 4) from both terms, we obtain:
(x + 4)(2x - 1) = 0
To find the values of x that solve the equation, we set each factor equal to zero and solve for x:
x + 4 = 0 --> x = -4
2x - 1 = 0 --> 2x = 1 --> x = 1/2
Therefore, the solutions to the equation 2x^2 + 7x - 4 = 0 are x = -4 and x = 1/2.