carmen is an electrician she charges an initial fee of $32 plus $33 per hour if carmen earned $197 on a job how long did the job
2 answers:
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I presume with this you meant to say you want this equation in <u>general form</u>, also known as vertex form, which is y = a(x - h)² + k, instead of <u>standard form</u>, which is y = ax² + bx + c, which is what the original equation is already in.
So with completing the square, you first have to isolate the x-terms. To do this, subtract 9 on both sides of the equation:
Next, we want to make the right side of the equation a perfect square. To find the constant of this soon-to-be perfect square, divide the x-coefficient by 2 and square that quotient. In this case:
Now add 25/4 on both sides of the equation:
Now to combine -9/1 and 25/4, they must have the same denominator, and to find it you must find the LCD, or lowest common denominator, of 1 and 4. To find it, list the multiples of both and the lowest one they share is their LCD. In this case, the LCD is 4. Multiply both sides of -9/1 by 4/4 and then add the numerators up:
Next, we need to factor the right side of the equation. Using this format of , we can factor it as:
Now lastly, add both sides by 11/4, and <u>your final answer will be </u>