Solving quadratics using square roots

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. For example, the square root of 121 is 11, since 11² = 121.

Front

How do you solve the equation x² = 121?

Back

To solve x² = 121, take the square root of both sides: x = ±√121, which gives x = ±11.

Front

What is the principle of isolating the variable in quadratic equations?

Back

Isolating the variable involves rearranging the equation to get the variable on one side and the constant on the other, allowing for easier solving.

Front

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

Back

Solving a quadratic equation using square roots involves rewriting the equation in the form x² = k and then taking the square root of both sides.

Front

Solve the equation x² + 4 = 68.

Back

x² = 68 - 4; x² = 64; x = ±8.

Front

What is the solution to the equation 4m² - 100 = 0?

Back

4m² = 100; m² = 25; m = ±5.

Front

How do you solve 5b² - 4 = 41?

Back

5b² = 41 + 4; 5b² = 45; b² = 9; b = ±3.

Front

What is the first step in solving the equation 7x² + 1 = 8?

Back

Subtract 1 from both sides: 7x² = 7.

Front

What is the solution to the equation 7x² = 7?

Back

x² = 1; x = ±1.

Front

Define 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.