Solve by factoring: x^2 + 5x = −6
Please help! I have a test next week and this is one of the practice problems and I do not understand this. I will not graduate unless I get a C. Please, Please!! Thank you
first of all, if you are going to factor an equation, get the RS equal to zero
x^2 + 5x + 6 = 0
Now can you think of 2 number, which when multiplied gives you 6, and which when added give you 5 ??
How about 2 and 3 ---> 2+3 = 5 and 2x3 = 6
so (x-2)(x-3) = 0
then x-2=0 or x-3 = 0
x = 2 or x = 3
Just an observation here, but you are not going to get any easier question along this topic than your question. You will just HAVE TO know how to do these.
To solve the equation x^2 + 5x = -6 by factoring, we need to rearrange the equation so that one side is equal to zero. Let's move all the terms to one side:
x^2 + 5x + 6 = 0
Now, we will factor the quadratic expression on the left side. We are looking for two numbers that multiply to give 6 and add up to give 5. These numbers are 2 and 3. Therefore, the factored form of the equation is:
(x + 2)(x + 3) = 0
To solve for x, we set each factor equal to zero and solve for x:
x + 2 = 0 or x + 3 = 0
Solving each of these equations will give us the solutions:
For x + 2 = 0, subtract 2 from both sides:
x = -2
For x + 3 = 0, subtract 3 from both sides:
x = -3
So, the solutions to the equation x^2 + 5x = -6 by factoring are x = -2 and x = -3.
To solve the equation x^2 + 5x = -6 by factoring, follow these steps:
Step 1: Rewrite the equation in standard form, where the right side is zero:
x^2 + 5x + 6 = 0
Step 2: Factor the quadratic expression on the left side. Look for two numbers that multiply to give +6 and add up to +5. In this case, the numbers are +2 and +3:
(x + 2)(x + 3) = 0
Step 3: Apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero:
x + 2 = 0 or x + 3 = 0
Step 4: Solve each equation separately:
For x + 2 = 0, subtracting 2 from both sides gives:
x = -2
For x + 3 = 0, subtracting 3 from both sides gives:
x = -3
Now, you have found the two values for x that satisfy the equation. Since x can be either -2 or -3, the solution to the equation x^2 + 5x = -6 is x = -2 or x = -3.
Remember, practicing more problems and familiarizing yourself with the factoring method will help you improve your skills and increase your chances of getting a good grade on your test. Good luck!