Square root method

Front

What is the Square Roots Method used for in algebra?

Back

The Square Roots Method is used to solve quadratic equations by isolating the variable and taking the square root of both sides.

Front

How do you isolate the variable in a quadratic equation using the Square Roots Method?

Back

To isolate the variable, rearrange the equation to the form x^2 = k, where k is a constant, and then take the square root of both sides.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What are the steps to solve the equation x^2 - 100 = 0 using the Square Roots Method?

Back

1. Add 100 to both sides to get x^2 = 100. 2. Take the square root of both sides to find x = ±10.

Front

What does the symbol ± mean in the context of solutions to quadratic equations?

Back

The symbol ± indicates that there are two possible solutions: one is the positive root and the other is the negative root.

Front

How do you solve the equation (x + 3)^2 - 13 = 0 using the Square Roots Method?

Back

1. Add 13 to both sides to get (x + 3)^2 = 13. 2. Take the square root of both sides to find x + 3 = ±√13. 3. Subtract 3 from both sides to get x = -3 ± √13.

Front

What is the solution to the equation 25x^2 = 4 using the Square Roots Method?

Back

1. Divide both sides by 25 to get x^2 = 4/25. 2. Take the square root of both sides to find x = ±2/5.

Front

What is the first step in solving a quadratic equation using the Square Roots Method?

Back

The first step is to isolate the x^2 term on one side of the equation.

Front

What are the solutions to the equation (x - 6)^2 = 31 using the Square Roots Method?

Back

1. Take the square root of both sides to get x - 6 = ±√31. 2. Add 6 to both sides to find x = 6 ± √31.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if it's positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.