write 3x^2 +8x-25 in the form a(x+h)^2,where a,h and k are real numbers
That expression is not a perfect square. You would have to add a constant. Maybe that is the "k" that you left out
3x^2 +8x -25 = 3(x^2 + 8x/3 -25/3)
= 3(x^2 + 8x/3 + 16/9) -25 - 48/9
= 3(x + 4/3)^2 - 123/9
To write the quadratic expression 3x^2 + 8x - 25 in the form a(x + h)^2, where a, h, and k are real numbers, we need to complete the square.
Step 1: Start with the given quadratic expression 3x^2 + 8x - 25.
Step 2: Focus on the x^2 and x terms only. Ignore the constant term (-25) for now.
Step 3: To complete the square, divide the coefficient of the x term (8) by 2, square the result, and add it to both sides of the equation:
3x^2 + 8x + (8/2)^2 = 25 + (8/2)^2
Simplifying this:
3x^2 + 8x + 16 = 41
Step 4: Now, we rewrite the left side of the equation as a perfect square trinomial:
3(x^2 + (8/3)x + (8/3)^2) = 41
Step 5: Rewrite the perfect square trinomial as (x + h)^2, where h is equal to half the coefficient of x:
3(x + 8/3)^2 = 41
Now, the expression 3x^2 + 8x - 25 is in the form a(x + h)^2, where a = 3 and h = 8/3.