Solving by Square roots

Front

What is the square root of a number?

Back

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, since 3 x 3 = 9.

Front

How do you solve an equation of the form (x - a)^2 = b?

Back

To solve (x - a)^2 = b, take the square root of both sides, resulting in x - a = ±√b. Then, solve for x by adding a to both sides: x = a ± √b.

Front

What does it mean if an equation has two solutions?

Back

An equation having two solutions means that there are two distinct values of the variable that satisfy the equation. This often occurs in quadratic equations.

Front

Solve: (x - 2)^2 = 49

Back

x = 2 ± 7, so x = 9 or x = -5.

Front

What is the principle of completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)^2 = q, making it easier to solve for x.

Front

Solve: -3(x + 4)^2 - 3 = -15

Back

x = -6 or x = -2.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation ax^2 + bx + c = 0, given by x = (-b ± √(b^2 - 4ac)) / (2a).

Front

Solve: (x - 2)^2 = 9

Back

x = 2 ± 3, so x = 5 or x = -1.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots of a quadratic equation are the x-intercepts of its graph. If the roots are real and distinct, the graph intersects the x-axis at two points.

Front

Solve: 3x^2 - 1 = 14

Back

3x^2 = 15, so x^2 = 5, giving x = ±√5.