Solving Quadratic Equations By Completing The Square

Front

What is the purpose of the plus or minus (±) symbol in solving quadratic equations?

Back

It indicates that there are two possible solutions after taking the square root of both sides.

Front

What is the first step in completing the square for the equation x² - 5x = 10?

Back

Rearrange the equation to x² - 5x - 10 = 0.

Front

How do you find the value to complete the square for the expression x² - 8x?

Back

Take half of -8 (which is -4) and square it to get 16.

Front

What is the completed square form of the equation x² - 12x + 4 = 20?

Back

(x - 6)² = 16.

Front

What does it mean to complete the square?

Back

It is a method used to convert a quadratic equation into a perfect square trinomial.

Front

What is a perfect square trinomial?

Back

It is an expression of the form (a + b)² = a² + 2ab + b².

Front

How do you solve the equation (x + 3)² = 49?

Back

Take the square root of both sides to get x + 3 = ±7, then solve for x.

Front

What is the solution to the equation x² - 5x = 10 after completing the square?

Back

x = 5/2 ± √(65/4).

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: two real and distinct, one real and repeated, or no real roots.