Solve the following quadratic equation by factoring.
x2+3x=18
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2
+
3
�
=
18
**Note: Please type your answers from least to greatest. For example, x1
�
1
would be the smallest solution and x2
�
2
would be your largest.
(1 point)
x1=
�
1
=
x2=
�
2
=
To solve the quadratic equation x^2 + 3x = 18, let's move all the terms to one side to get:
x^2 + 3x - 18 = 0
Next, we can factor the quadratic expression:
(x + 6)(x - 3) = 0
Setting each factor equal to zero, we get:
x + 6 = 0 or x - 3 = 0
Solving for x in each equation gives:
x = -6 or x = 3
Therefore, the solutions to the quadratic equation are:
x1 = -6
x2 = 3
To solve the quadratic equation by factoring, we need to rewrite the equation in the form of a quadratic expression equal to zero.
The given equation is x^2 + 3x - 18 = 0.
Step 1: Factor the quadratic expression.
We are looking for two numbers whose product is -18 and whose sum is 3. After trying different combinations, we find that 6 and -3 satisfy these conditions.
So, we can rewrite the equation as (x + 6)(x - 3) = 0.
Step 2: Set each factor equal to zero and solve for x.
Setting (x + 6) = 0, we get x = -6.
Setting (x - 3) = 0, we get x = 3.
Therefore, the solutions to the equation x^2 + 3x - 18 = 0, obtained by factoring, are x1 = -6 and x2 = 3.
To solve the quadratic equation x^2 + 3x - 18 = 0 by factoring, we need to find two numbers that satisfy the following conditions:
1. Multiply to give the product of the coefficient of x^2 (1) and the constant term (-18), which is -18.
2. Add up to give the coefficient of x, which is 3.
After considering all the possible combinations, we find that the numbers are 6 and -3:
6 * (-3) = -18
6 + (-3) = 3
Now we can factor the equation as follows:
(x + 6)(x - 3) = 0
From here, we set each factor equal to zero and solve for x:
x + 6 = 0
=> x = -6
x - 3 = 0
=> x = 3
So the solutions to the quadratic equation x^2 + 3x - 18 = 0, when factored, are x1 = -6 and x2 = 3.