Solve the following quadratic equation by factoring. x2+3x=18 **Note: Please type your answers from least to greatest. For example, x1 would be the smallest solution and x2 would be your largest. (1 point) show all your work
To solve the quadratic equation x^2 + 3x = 18 by factoring, we need to rearrange the equation to equal zero.
x^2 + 3x - 18 = 0
Now we will attempt to factor the quadratic expression on the left-hand side of the equation.
The factors of -18 that could sum up to 3 (the coefficient of x) are 6 and -3.
(x + 6)(x - 3) = 0
Now we set each factor equal to zero and solve for x.
x + 6 = 0
x = -6
x - 3 = 0
x = 3
Therefore, the solutions to the quadratic equation x^2 + 3x = 18 are x = -6 and x = 3.
To solve the quadratic equation x^2 + 3x = 18 by factoring, we need to rearrange the equation so that one side is equal to zero.
Step 1: Move all the terms to one side:
x^2 + 3x - 18 = 0
Step 2: Factor the quadratic expression on the left side:
(x + 6)(x - 3) = 0
Now we have factored the equation into two binomial expressions equal to zero.
Step 3: Set each binomial factor equal to zero and solve for x:
x + 6 = 0 or x - 3 = 0
If x + 6 = 0, then x = -6
If x - 3 = 0, then x = 3
So the solutions to the quadratic equation x^2 + 3x = 18 are x = -6 and x = 3.
To solve the quadratic equation x^2 + 3x = 18 by factoring, we need to rewrite the equation in standard quadratic form, which is ax^2 + bx + c = 0.
So, let's move all the terms to one side of the equation:
x^2 + 3x - 18 = 0
Now, we can look for two numbers, let's call them a and b, such that their product is equal to the product of "a" and "c" in the quadratic equation.
The product of "a" and "c" is -18. We need to find two numbers whose product is -18 and whose sum is 3 (since the coefficient of x is 3).
Let's try the factor pairs of -18: (-1, 18), (1, -18), (-2, 9), (2, -9), (-3, 6), and (3, -6).
After trying these factor pairs, we find that (-3, 6) satisfies both the conditions.
Therefore, we can rewrite the equation as:
(x - 3)(x + 6) = 0
Now, we can solve for x by setting each factor equal to zero:
x - 3 = 0 or x + 6 = 0
Solving for x in the first equation:
x - 3 = 0
x = 3
And solving for x in the second equation:
x + 6 = 0
x = -6
Hence, the solutions to the quadratic equation x^2 + 3x = 18 are x = -6 and x = 3.
So, the answers are x1 = -6 and x2 = 3.