Solve Quadratic Equations by Taking Square Roots

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to solve a quadratic equation by taking square roots?

Back

Solving a quadratic equation by taking square roots involves isolating the squared term and then applying the square root to both sides, resulting in two possible solutions (positive and negative).

Front

What is the first step in solving the equation x² = 12?

Back

The first step is to isolate x², which is already done in this case. Then, take the square root of both sides.

Front

What is the solution to the equation x² = 12?

Back

The solution is x = ±2√3.

Front

How do you simplify the expression √(2x²)?

Back

You can simplify it to x√2, assuming x is non-negative.

Front

What is the significance of the ± symbol when solving quadratic equations?

Back

The ± symbol indicates that there are two possible solutions: one positive and one negative.

Front

How do you solve the equation 2x² = 100?

Back

First, divide both sides by 2 to get x² = 50, then take the square root to find x = ±5√2.

Front

What is the solution set for the equation (x - 14)² = 36?

Back

The solution set is {8, 20}.

Front

What is the process for solving x² - 49 = 0?

Back

Factor the equation as (x - 7)(x + 7) = 0, leading to the solutions x = -7 and x = 7.

Front

When do you use the square root method to solve a quadratic equation?

Back

You use the square root method when the equation can be expressed in the form x² = k, where k is a constant.