write 3x*2+8x-25 in the form a(x+h)*2+k where a,h and k are real numbers
formulae for h=b/2a
formulae for k=4ac-b^2/4a
h=8/2*3=1.33
4 (3)+ (-25)-8*2/4*3=-152/12=12.6
3(x-12.6)^2=1.33/3
x-12.6=+-0.67
x=0.67+3.55=4.22
x=-0.67+3.55=2.88
Correct.
Idon't know!!! that's tooo hard!!
To write the expression 3x^2 + 8x - 25 in the form a(x + h)^2 + k, where a, h, and k are real numbers, we can follow these steps:
Step 1: Group the quadratic terms (terms with x^2 and x) together.
In this case, we have 3x^2 + 8x.
Step 2: Find the coefficient of x^2.
In this case, the coefficient of x^2 is 3.
Step 3: Calculate the value of h using the formula h = -b / (2a).
Using the coefficient of x (8) and the coefficient of x^2 (3), we get h = -8 / (2 * 3) = -8 / 6 = -4 / 3 ≈ -1.33.
Step 4: Calculate the value of k using the formula k = 4ac - b^2 / (4a).
Using the coefficient of x^2 (3), the coefficient of x (8), and the constant term (-25), we get k = 4 * 3 * (-25) - 8^2 / (4 * 3) = -300 - 64 / 12 = -364 / 12 ≈ -30.33.
Step 5: Plug the values of h and k into the equation a(x + h)^2 + k.
The equation becomes 3(x - 4/3)^2 - 364/12.
Note: There seems to be a calculation mistake in the provided solution for the value of k. Instead of getting -152/12, it should be -364/12 as shown above.
To find the solutions of the quadratic equation, we can set the expression equal to zero and solve for x.
3(x - 4/3)^2 - 364/12 = 0
Simplifying, we get:
3(x - 4/3)^2 = 364/12
Dividing both sides by 3:
(x - 4/3)^2 = 364/36
Taking the square root of both sides:
x - 4/3 = ±√(364/36)
Simplifying the square root:
x - 4/3 = ±(√(364)/√(36))
x - 4/3 = ±(√(364)/6)
Adding 4/3 to both sides:
x = 4/3 ± (√(364)/6)
Simplifying further:
x = 4/3 + (√(364)/6) ≈ 4.22
x = 4/3 - (√(364)/6) ≈ 2.88
So, the solutions to the quadratic equation 3x^2 + 8x - 25 in the form a(x + h)^2 + k are approximately x = 4.22 and x = 2.88.