Solving Quadratics by 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 by square roots?

Back

Solving a quadratic equation by 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 number?

Back

The square root of a number x is a value y such that y² = x.

Front

How do you isolate x² in the equation k² - 6 = 43?

Back

Add 6 to both sides to get k² = 49.

Front

What are the solutions to the equation k² = 49?

Back

k = 7 and k = -7.

Front

What is the first step in solving 4x² - 25 = 0?

Back

Add 25 to both sides to get 4x² = 25.

Front

How do you solve for x in the equation 4x² = 25?

Back

Divide both sides by 4 to get x² = 25/4, then take the square root.

Front

What are the solutions to the equation x² = 25/4?

Back

x = 5/2 and x = -5/2.

Front

How do you solve the equation 5b² - 4 = 41?

Back

Add 4 to both sides to get 5b² = 45, then divide by 5.

Front

What is the value of b when solving 5b² = 45?

Back

b² = 9, so b = 3 and b = -3.