Find the smallest value of x such that x^2+6x + 9 = 24
Please help me! I am very confused. Thank you!
surely you have learned how to solve a quadratic equation, or you'd not have been given this exercise.
x^2+6x + 9 = 24
x^2+6x-15 = 0
x = (-6±√96)/2 = -3±2√6
clearly, -3-2√6 is less than -3+2√6
To find the smallest value of x that satisfies the equation x^2 + 6x + 9 = 24, we can start by subtracting 24 from both sides of the equation:
x^2 + 6x + 9 - 24 = 0
Combining like terms, we get:
x^2 + 6x - 15 = 0
Now, we need to factorize the quadratic equation. We can rewrite it as:
(x + 5)(x - 3) = 0
Now, we can set each factor equal to zero and solve for x:
x + 5 = 0 or x - 3 = 0
For the first equation, subtract 5 from both sides:
x = -5
For the second equation, add 3 to both sides:
x = 3
So, the possible solutions are x = -5 and x = 3. To find the smallest value of x that satisfies the equation, we take the smaller of the two values, which is x = -5. Therefore, the smallest value of x is -5.
Sure! I can help you with that.
To find the smallest value of x that satisfies the equation x^2 + 6x + 9 = 24, we'll need to solve the equation for x by rearranging the terms and simplifying it.
Let's start by subtracting 24 from both sides of the equation to isolate the x^2 term:
x^2 + 6x + 9 - 24 = 0
After simplifying, we get:
x^2 + 6x - 15 = 0
Now, we can use the quadratic formula to solve the equation for x. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 6, and c = -15. Substituting the values into the quadratic formula, we get:
x = (-6 ± √(6^2 - 4(1)(-15))) / (2(1))
Simplifying further:
x = (-6 ± √(36 + 60)) / 2
x = (-6 ± √96) / 2
Now, let's simplify the square root:
x = (-6 ± √(16 * 6)) / 2
x = (-6 ± 4√6) / 2
We can simplify the expression:
x = (-3 ± 2√6)
So, we have two possible solutions for x: -3 + 2√6 and -3 - 2√6.
However, we want to find the smallest value of x. In this case, it will be the negative solution: -3 - 2√6.
Therefore, the smallest value of x that satisfies the equation x^2 + 6x + 9 = 24 is approximately -6.5.
I hope this explanation helps! Let me know if you have any further questions.