Solving Quadratic Using 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 using square roots?

Back

Solving a quadratic equation using square roots involves isolating the squared term and then taking the square root of both sides to find the variable's values.

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. It can be positive or negative.

Front

How do you isolate a squared term in an equation?

Back

To isolate a squared term, you move all other terms to the opposite side of the equation.

Front

What is the first step in solving 5b² - 4 = 41?

Back

Add 4 to both sides to isolate the term with b²: 5b² = 45.

Front

What is the next step after isolating the squared term?

Back

Divide both sides by the coefficient of the squared term to solve for b².

Front

How do you find the values of b in the equation 5b² = 45?

Back

Divide by 5 to get b² = 9, then take the square root: b = ±3.

Front

What is the solution to (x+3)² - 5 = 9?

Back

First, isolate (x+3)² to get (x+3)² = 14, then take the square root: x + 3 = ±√14.

Front

What does ± mean in solutions?

Back

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

Front

How do you solve (x-5)² = 25?

Back

Take the square root of both sides: x - 5 = ±5, leading to x = 10 or x = 0.