Solve the quadratic by factoring.
x, squared, plus, 10, x, equals, minus, 4, x, minus, 40
x
2
+10x=−4x−40
To solve this quadratic equation by factoring, we need to set the equation equal to zero.
Starting with the given equation:
x^2 + 10x = -4x - 40
Let's bring all the terms to the left side:
x^2 + 10x + 4x + 40 = 0
Combining like terms:
x^2 + 14x + 40 = 0
Now, we need to find two numbers whose sum is 14 and whose product is 40. Those numbers are 4 and 10.
So, we can rewrite the equation as:
x^2 + 4x + 10x + 40 = 0
Now, we group the terms:
(x^2 + 4x) + (10x + 40) = 0
Factoring out the greatest common factor from each group:
x(x + 4) + 10(x + 4) = 0
Now, notice that we have a common binomial, (x + 4). We can take it out as a common factor:
(x + 4)(x + 10) = 0
Now, we can set each factor equal to zero and solve for x:
x + 4 = 0 or x + 10 = 0
Solving for x in each equation:
x = -4 or x = -10
So, the solutions to the quadratic equation are x = -4 and x = -10.
To solve the quadratic equation by factoring, we need to rearrange the equation and set it equal to zero.
In this case, the equation is:
x^2 + 10x = -4x - 40
Step 1: Simplify
Combine like terms on both sides of the equation:
x^2 + 10x + 4x + 40 = 0
Step 2: Arrange in standard form
Rearrange the equation to have all terms on one side equal to zero:
x^2 + 14x + 40 = 0
Step 3: Factor the quadratic expression
To factor the expression x^2 + 14x + 40, we need to find two numbers that multiply to give 40 and add up to give 14. Those numbers are 4 and 10.
Step 4: Write the factored form
We can now write the equation in factored form:
(x + 4)(x + 10) = 0
Step 5: Set each factor equal to zero
Set each factor equal to zero and solve for x:
x + 4 = 0 or x + 10 = 0
Step 6: Solve for x
Solve each equation separately:
For x + 4 = 0:
x = -4
For x + 10 = 0:
x = -10
Therefore, the solutions to the quadratic equation x^2 + 10x = -4x - 40 are x = -4 and x = -10.
To solve the quadratic equation x^2 + 10x = -4x - 40 by factoring, follow these steps:
1. Start by rearranging the equation to bring all terms to one side:
x^2 + 10x + 4x + 40 = 0
2. Combine like terms in the middle:
x^2 + 14x + 40 = 0
3. Now, we need to factor the quadratic expression. Determine two numbers whose product is equal to the constant term (40) and whose sum is equal to the coefficient of the middle term (14). In this case, we have:
4 * 10 = 40
4 + 10 = 14
4. Rewrite the middle term using the two numbers found in the previous step:
x^2 + 4x + 10x + 40 = 0
5. Group the terms and factor by grouping:
(x^2 + 4x) + (10x + 40) = 0
x(x + 4) + 10(x + 4) = 0
6. Notice that (x + 4) is common to both terms, so factor it out:
(x + 4)(x + 10) = 0
7. Set each factor equal to zero and solve for x:
x + 4 = 0 --> x = -4
x + 10 = 0 --> x = -10
Therefore, the solutions to the quadratic equation x^2 + 10x = -4x - 40 are x = -4 and x = -10.