Samantha needs to solve the equation
x2 - 12x = 40.
What must she do to each side of the
equation to complete the square?
"^" is used online to indicate an exponent. "complete the square"?
Subtract 40 from both sides.
x^2 - 12 - 40 = 0
From there you should be able to factor. However, using the possible factors of -40 (4,10; 8,5; etc.), I don't see how that will give -12 as a middle term. Do you have a typo?
To complete the square, Samantha must add a constant term to both sides of the equation. The constant term is half the coefficient of the x-term squared. In this case, the coefficient of the x-term is -12, so half of it is -6. To complete the square, she needs to add (-6)^2 = 36 to both sides of the equation.
To complete the square, Samantha needs to follow these steps:
Step 1: Move the constant term to the other side of the equation:
x^2 - 12x - 40 = 0.
Step 2: Set up the equation with a placeholder term and square it:
(x - b)^2 = c.
To find the value of 'b,' take half of the coefficient of the linear term and square it. In this case, the coefficient of x is -12. So, take half of -12 and square it:
(-12/2)^2 = 36.
Step 3: Add the squared term on both sides of the equation:
x^2 - 12x + 36 - 40 = 36 - 40.
Simplify: x^2 - 12x - 4 = 0.
Step 4: Factor the perfect square trinomial:
(x - 6)^2 = 40.
Now, Samantha has completed the square of the equation x^2 - 12x = 40.