Solve by factoring: x^2 + 7x + 10 = 0
On this specific example my text isn't helping....thanks!
(x + a ) (x + b) = x^2 + 7x + 10
Think what two number multiplied give 10, and when added give 7?
what is factoral equations????
To solve the quadratic equation x^2 + 7x + 10 = 0 by factoring, we need to find two binomials that, when multiplied, equal the given quadratic equation. Here's how to do it:
Step 1: Write down the equation: x^2 + 7x + 10 = 0.
Step 2: Look for two numbers, let's call them "a" and "b", such that their sum is equal to the coefficient of the middle term (7) and their product is equal to the product of the coefficient of the first term (1) and the constant term (10).
In this case, we're looking for two numbers that add up to 7 and multiply to 10. The numbers that fulfill these conditions are 2 and 5.
Step 3: Rewrite the middle term (7x) as the sum of the two numbers found in Step 2. So, replace 7x with 2x + 5x. The equation becomes: x^2 + 2x + 5x + 10 = 0.
Step 4: Group the terms together, as follows: (x^2 + 2x) + (5x + 10) = 0.
Step 5: Factor out the greatest common factor from each group. In this case, we can factor out an "x" from the first group and a "5" from the second group. The equation becomes: x(x + 2) + 5(x + 2) = 0.
Step 6: Notice that we have a common binomial factor of (x + 2). Factor it out: (x + 2)(x + 5) = 0.
Step 7: Set each factor equal to zero and solve for x:
x + 2 = 0 --> x = -2
x + 5 = 0 --> x = -5
So, the solutions to the equation x^2 + 7x + 10 = 0 are x = -2 and x = -5.