Solving Quadratics by Square Roots

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 solve a quadratic equation by taking square roots?

Back

To solve a quadratic equation of the form x² = a, take the square root of both sides, resulting in x = ±√a.

Front

Solve by taking the square root: 4x² = 100

Back

x = ±5

Front

What is the solution for x in the equation -9p² = -576?

Back

x = 8, -8

Front

Solve for a: a² + 9 = 9

Back

a = 0

Front

What is the first step to solve (x - 7)² + 4 = 40?

Back

Subtract 4 from both sides to isolate the squared term: (x - 7)² = 36.

Front

What are the solutions for x in the equation (x - 7)² + 4 = 40?

Back

x = 1, 13

Front

Solve for x: x² - 4 = 77

Back

x = ±9

Front

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

Back

It means that the equation does not intersect the x-axis, often resulting from a negative discriminant.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots.