Quadratic Equations: Completing the Square

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

• Multiply by the coefficient of x

• Divide by the coefficient of x squared

• Add a constant to both sides

• Get rid of the constant term

How do you find the value of c when completing the square?

• Add the coefficient of x to the constant

• Multiply the coefficient of x by 2

• Subtract the constant from the coefficient of x

• Divide the coefficient of x by 2 and square it

What is the purpose of taking the square root on both sides of the equation?

• To eliminate the constant term

• To factor the trinomial

• To simplify the equation

• To solve for x

In the second example, why is it necessary to divide by the coefficient of x squared?

• To factor the trinomial

• To eliminate the constant term

• To simplify the equation

• To make the coefficient of x squared equal to 1

What is the result of rationalizing the denominator in the second example?

• A simpler fraction

• A radical expression

• An integer

• A complex number

How do you determine the two solutions for x in the final example?

• By adding and subtracting the square root term

• By multiplying the square root term

• By dividing the square root term

• By factoring the square root term

What is the value of c in the final example problem?

• 16/49

• 25/4

• 49/16

• 7/4

Why is it important to have the same denominator when adding fractions in the final example?

• To simplify the equation

• To ensure the fractions are like terms

• To factor the trinomial

• To eliminate the constant term

What is the final step in solving the quadratic equation in the last example?

• Adding the square root term to both sides

• Dividing by the coefficient of x

• Subtracting the constant from both sides

• Adding the constant to both sides

How can you verify the solutions obtained from the quadratic equation?

• By checking if they satisfy the original equation

• By multiplying them together

• By adding them to the coefficient of x

• By comparing them to the constant term