Question

When 2x^2-20x+49=19 is written in the form (x-p)^2=q what is the value of q

Answer 1

To find the desired form of the equation, we need to complete the square.

Step 1: Subtract 19 from both sides:
2x^2 - 20x + 49 - 19 = 0
2x^2 - 20x + 30 = 0

Step 2: Factor out the common factor, 2 from the first two terms:
2(x^2 - 10x) + 30 = 0

Step 3: Take half of the coefficient of the x-term, which is -10, and square it:
(-10/2)^2 = (-5)^2 = 25

Step 4: Add the result from step 3 to both sides of the equation:
2(x^2 - 10x + 25) + 30 - 50 = 0
2(x - 5)^2 + 30 - 50 = 0

Step 5: Simplify:
2(x - 5)^2 - 20 = 0

So, when 2x^2 - 20x + 49 = 19 is written in the form (x - p)^2 = q, the value of q is 20.