Solving Quadratic Equations by Completing the Square

The video tutorial explains how to solve quadratic equations by completing the square when the coefficient of x squared is greater than one. It provides a step-by-step guide, including rearranging terms, dividing by the coefficient, and creating a perfect square trinomial. The tutorial includes four examples, demonstrating the process of solving and simplifying quadratic equations, with both approximate and exact solutions.

What is the primary goal of completing the square in quadratic equations?

• To simplify the equation to its basic form

• To eliminate the constant term

• To create a binomial squared

• To isolate the x term

What is the first step in solving a quadratic equation by completing the square when a > 1?

• Isolate the constant on one side

• Divide the equation by the coefficient of x squared

• Rearrange the equation to get x terms on one side

• Factor the quadratic directly

In the example with a coefficient of 2, what value is added to both sides to complete the square?

• 4

• 16

• 2

• 8

What are the solutions to the quadratic equation where the initial setup was x squared minus 4x equals -3?

• x = 1, 3

• x = -1, -3

• x = 0, 2

• x = 2, 4

After dividing by the coefficient, what is the next step in completing the square?

• Add the square of half the coefficient of x to both sides

• Subtract the square of half the coefficient of x from both sides

• Multiply each term by the coefficient of x squared

• None of the above

What does x minus 3 squared equal to after completing the square for the equation 4x squared minus 24x equals 64?

• 25

• 16

• 9

• 49

How do you simplify the square root of 28 to get an exact answer?

• 2 square root of 7

• 3 square root of 7

• 4 square root of 7

• 5 square root of 7

What is the approximate decimal solution for x in the equation x plus 5 squared equals 28?

• x ≈ -7.29, 2.29

• x ≈ -5.29, 5.29

• x ≈ -10.29, 0.29

• x ≈ -8.29, 3.29

What is the result of x plus 3 squared equals 13 solved using the square roots method?

• x = 3 ± √10

• x = -3 ± √13

• x = 3 ± √13

• x = -3 ± √10

What is the simplified form of the square root of 13?

• 4√13

• 3√13

• 2√13

• √13