Solving Quadratics by 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

Solving a quadratic equation by taking square roots involves isolating the x² term and then applying the square root to both sides of the equation.

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. It can be positive or negative.

Front

How do you isolate x² in the equation x² - 3 = 78?

Back

Add 3 to both sides to get x² = 81.

Front

What are the solutions to the equation x² = 81?

Back

The solutions are x = 9 and x = -9.

Front

What is the first step in solving the equation 5m² + 1 = 6?

Back

Subtract 1 from both sides to get 5m² = 5.

Front

How do you solve for m in the equation 5m² = 5?

Back

Divide both sides by 5 to get m² = 1, then take the square root.

Front

What are the solutions to the equation m² = 1?

Back

The solutions are m = 1 and m = -1.

Front

What is the process to solve k² - 6 = 43?

Back

Add 6 to both sides to get k² = 49, then take the square root.

Front

What are the solutions to the equation k² = 49?

Back

The solutions are k = 7 and k = -7.