Samantha needs to solve the equation
x2 - 12x = 40.
What must she do to each side of the
equation to complete the square?
Samantha must add 36 to each side of the equation to complete the square.
To complete the square, Samantha needs to add a constant to both sides of the equation. The constant she needs to add is half of the coefficient of the 'x' term (which is -12 in this case) squared. In other words, she needs to add ((-12/2)^2) to both sides of the equation.
Let's break it down step-by-step:
1. Start with the equation:
x^2 - 12x = 40
2. Find the constant to be added by taking half of the coefficient of the 'x' term:
(-12/2)^2 = 6^2 = 36
3. Add the constant (36) to both sides of the equation:
x^2 - 12x + 36 = 40 + 36
4. Simplify:
x^2 - 12x + 36 = 76
Now, Samantha has completed the square.
To complete the square for the equation x² - 12x = 40, Samantha must follow these steps:
Step 1: Move the constant term to the right side of the equation.
x² - 12x + ___ = 40 + ___
Step 2: Take half the coefficient of the x-term, square it, and add it to both sides of the equation.
x² - 12x + (-12/2)² = 40 + (-12/2)²
x² - 12x + 36 = 40 + 36
Step 3: Simplify both sides of the equation.
x² - 12x + 36 = 76
Step 4: Factor the perfect square trinomial on the left side of the equation.
(x - 6)² = 76
Now, Samantha has completed the square for the equation x² - 12x = 40, which resulted in (x - 6)² = 76.