Find the length of a side of a square if its area is 9ײ+30×+25.
area = 9x²+30x+25
side = √(9x²+30x+25)
= √(3x+5)^2
= 3x+5, where x > -5/3
Since all we know is that 3x+5 > 0, maybe we should consider that
√(3x+5)^2 = |3x+5|
doesn't really matter what x is.
Find the length of a side (s)of a square if it's area (a) is 9ײ+30 ×+25
Well, if we have to find the length of a side of a square with area 9ײ + 30× + 25, we need to take the square root of that expression. So, what's the square root of 9ײ + 30× + 25?
Hmm, let's see... I don't have a calculator with me, but I bet it's the same thing as trying to find your car keys in the darkest corner of a room filled with clowns. It's a bit tricky, but let's give it a shot!
Using the quadratic formula, we can determine that the roots of the equation 9ײ + 30× + 25 = 0 are going to be some really ugly, irrational numbers. But hey, that's what happens when you invite clowns to a math party, right?
In conclusion, finding the length of that square's side is like trying to wrangle a bunch of clown noses. It's a real circus act!
To find the length of a side of a square, we need to take the square root of its area. In this case, the area is given by the polynomial 9x² + 30x + 25.
Step 1: Rewrite the polynomial in factored form.
To factor the polynomial 9x² + 30x + 25, we need to find two binomials that multiply to give this polynomial. The factored form will be in the form (ax + b)(cx + d).
So, let's set up the equation and solve for a, b, c, and d:
(ax + b)(cx + d) = 9x² + 30x + 25
By expanding the right side and comparing coefficients, we find:
ac = 9 (from the x² terms)
ad + bc = 30 (from the x terms)
bd = 25 (from the constant terms)
Step 2: Determine the values of a, b, c, and d.
We need to find two numbers that multiply to give 9 and add up to 30. The numbers that satisfy this condition are 3 and 3. Therefore, our values for a and c are 3.
Now, we need to find two numbers that multiply to give 25. The numbers that satisfy this condition are 5 and 5. Therefore, our values for b and d are 5.
So, our factored form becomes:
(3x + 5)(3x + 5)
Step 3: Take the square root to find the side length.
Now that we have the factored form, we can find the square root. The square root of (3x + 5)² is 3x + 5.
Therefore, the length of a side of the square is 3x + 5.