How do you complete the square by filling in the two blanks so as to produce a true equation.
x^2 - 12x + ---- = (x - -----)^2
The first blank will have a 36 in it. The second blank will have 6 in it.
When you complete the square in this format, take half of the number in front of x, (called coefficient), and square it. So, in your case, the number in front of x is -12. If I take half of it, it is -6. Then, if I square it, the final result is +36. That goes in the first blank completing the trinomial on the left --> x^2 - 12x + 36
Now, the squared binomial on the right will use the half of the coefficient value. Thus, (x-6)^2 is the final answer on the right.
If you want to check your result, take the (x-6)^2 binomial, and rewrite it as a repeated factor: (x-6)(x-6). Perform FOIL, and you should get x^2 - 12x + 36.
WARNING: Completing the Square only works when the coefficient of the x^2 term is ONE!
Hope this helps!
Yes you helped me a lot. Thank you for showing me in steps how to solve this question
x^2-18x+___=( )^2
Find the value of t x^+t+16
To complete the square, we need to find the values that will fill in the blanks and make the equation true. Here's how to do it step by step:
Step 1: Begin with the equation:
x^2 - 12x + ---- = (x - -----)^2
Step 2: To complete the square, we need to take half of the coefficient of x, square it, and add it to both sides of the equation. The coefficient of x in this case is -12, so half of it is -6, and squaring it gives us 36. We add 36 to both sides:
x^2 - 12x + 36 = (x - -----)^2 + 36
Step 3: Simplify the right side of the equation by expanding the squared binomial:
x^2 - 12x + 36 = x^2 - 2*x*------ + -----^2 + 36
Step 4: Since we want the right side to be in the form (x - a)^2, we need to rewrite the middle term -2*x*----- as -2*-----*x, where ----- represents the value that will complete the square. So, we have:
x^2 - 12x + 36 = x^2 - 2*-----*x + -----^2 + 36
Step 5: Comparing the left side and the right side, we see that -2*-----*x must be equal to -12x, which means ----- must be equal to 6. So, we substitute 6 for -----:
x^2 - 12x + 36 = x^2 - 2*6*x + 6^2 + 36
Simplifying further:
x^2 - 12x + 36 = x^2 - 12x + 36
Step 6: Now we have a true equation, and we can see that the value to fill in the first blank is 36, and the value to fill in the second blank is 6. Therefore, the completed square equation is:
x^2 - 12x + 36 = (x - 6)^2