Solving Quadratics by Taking Square Roots

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form 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

It means isolating the x² term and then applying the square root to both sides of the equation to find the values of x.

Front

What is the square root of a number?

Back

The square root of a number x is a value y such that y² = x.

Front

How do you isolate a variable in a quadratic equation?

Back

To isolate a variable, you rearrange the equation to get the variable on one side and the constant on the other.

Front

What is the first step in solving the equation 5b² - 4 = 41?

Back

Add 4 to both sides to isolate the term with b²: 5b² = 45.

Front

What do you do after isolating the b² term in the equation 5b² = 45?

Back

Divide both sides by 5 to get b² = 9.

Front

What are the solutions to the equation b² = 9?

Back

The solutions are b = 3 and b = -3.

Front

What is the principle of taking square roots in solving equations?

Back

The principle states that if x² = a, then x = ±√a.

Front

How do you solve the equation 4m² - 100 = 0?

Back

Add 100 to both sides to get 4m² = 100, then divide by 4 to find m² = 25.

Front

What are the solutions to the equation m² = 25?

Back

The solutions are m = 5 and m = -5.