Solving Quadratics by Square Root Method

Front

What is the square root method for solving quadratics?

Back

The square root method involves isolating the squared term and then taking the square root of both sides to find the variable's value.

Front

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

Back

Subtract 1 from both sides to isolate the squared term: 7x² = 7.

Front

How do you isolate x² in the equation 7x² = 7?

Back

Divide both sides by 7 to get x² = 1.

Front

What are the possible values of x when x² = 1?

Back

x = ±1.

Front

What is the general form of a quadratic equation?

Back

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

Front

How do you solve x² + 4 = 68 using the square root method?

Back

Subtract 4 from both sides to get x² = 64, then take the square root to find x = ±8.

Front

What is the solution set for the equation 5b² - 4 = 41?

Back

First, add 4 to both sides to get 5b² = 45, then divide by 5 to find b² = 9, leading to b = ±3.

Front

What does it mean if a quadratic equation has no real solution?

Back

It means that the expression under the square root (the discriminant) is negative.

Front

How do you solve k² - 6 = 43?

Back

Add 6 to both sides to get k² = 49, then take the square root to find k = ±7.

Front

What is the solution to the equation 3x² = 12?

Back

Divide both sides by 3 to get x² = 4, then take the square root to find x = ±2.