Solving Quadratic Using 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 using square roots?

Back

Solving a quadratic equation using square roots involves isolating the x² term and then taking the square root of both sides to find the values of x.

Front

What is the square root of a negative number?

Back

The square root of a negative number is not a real number; it is an imaginary number, represented as i√|x|.

Front

How do you isolate x² in the equation -5x² = -50?

Back

Divide both sides by -5 to get x² = 10.

Front

What are the solutions to the equation x² = 10?

Back

The solutions are x = ±√10.

Front

How do you solve (x+3)² - 5 = 9?

Back

First, add 5 to both sides to get (x+3)² = 14, then take the square root to find x = ±√14 - 3.

Front

What are the solutions to the equation 3 + 9r² = 12?

Back

Subtract 3 from both sides to get 9r² = 9, then divide by 9 to find r² = 1, leading to r = ±1.

Front

How do you solve (x-5)² = 25?

Back

Take the square root of both sides to get x - 5 = ±5, leading to x = 10 or x = 0.

Front

What is the solution to the equation x² = 81?

Back

The solutions are x = ±9.

Front

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

Back

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