Solving Quadratics using Square Roots

Front

What is the Square Roots Method in solving quadratics?

Back

The Square Roots Method involves isolating the variable squared on one side of the equation and then taking the square root of both sides to solve for the variable.

Front

How do you solve the equation -9p^2 = -576?

Back

First, divide both sides by -9: p^2 = 64. Then take the square root: p = ±8.

Front

What are the solutions for the equation 25x^2 = 4?

Back

x = ±\frac{2}{5}.

Front

How do you solve (h - 2)^2 = 9?

Back

Take the square root of both sides: h - 2 = ±3. Thus, h = 5 or h = -1.

Front

What is the first step in solving the equation 4x^2 - 30 = 22?

Back

Add 30 to both sides to isolate the term with x^2: 4x^2 = 52.

Front

What are the solutions for the equation 5b^2 - 4 = 41?

Back

First, add 4 to both sides: 5b^2 = 45. Then divide by 5: b^2 = 9. Finally, take the square root: b = ±3.

Front

What is the general form of a quadratic equation?

Back

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

Front

What does it mean to take the square root of both sides of an equation?

Back

Taking the square root of both sides means finding a value that, when squared, gives the original value on each side of the equation.

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 positive, two real roots; if zero, one real root; if negative, no real roots.

Front

How do you isolate a squared term in an equation?

Back

To isolate a squared term, you can add or subtract other terms from both sides of the equation until the squared term is alone on one side.