Completing the Square and the Quadratic Formula

• True

• False

Answer explanation

True because completing the square involves transforming the equation into the form x^2 + bx = c before proceeding with the method.

What is the 1^st step in solving a Quadratic Equation using Completing the Square

• Divide b by 2

• Square root both sides

• Make sure the equation equals 0

• Get the terms containing the variables on one side of the equation

Answer explanation

Get the terms containing the variables on one side of the equation.

What do you do to the b value to correctly complete the square?

• square it

• divide it by 2 and square the result

• divide it by 2 and take the square root of the result

• divide it by 2 only

Answer explanation

To correctly complete the square, you need to divide the b value by 2 and then square the result. This process helps in simplifying the quadratic expression.

What is the first step to solving THIS equation by completing the square?
x² + 8x + 9 = 0

• Set the equation equal to zero

• Divide 8 by 2 and add the result to both sides

• Add x² and 8x together

• Subtract 9

Answer explanation

Subtract 9

Answer explanation

The correct choice is (x+4)^2=7 because completing the square involves halving the coefficient of x, squaring it, and adding/subtracting it to both sides of the equation.

Answer explanation

To solve the equation x^2 + 10x = 39, we first rearrange it to x^2 + 10x - 39 = 0. Then, factor or use the quadratic formula to find x = 3 or x = -13.

Answer explanation

To solve by completing the square, rewrite the equation as (x-6)^2=16. Then, solve for x to get x={2, 10}.

What are the solutions to this equation?

(2x - 1)² = 49

• x= -7, 8

• x= -4, 5

• x= -4, 3

• x= -3, 4

Answer explanation

To solve the equation (2x - 1)^2 = 49, first take the square root of both sides to get 2x - 1 = ±7. Then solve for x to get x = -3, 4. Therefore, the correct solutions are x = -3, 4.

• 19

• 10

• 5

• -30

Answer explanation

To rewrite the equation in the form (x-p)^2=q, complete the square by finding p and q. The value of q is the constant term in the completed square form, which is 10. Therefore, the correct answer is 10.

Answer explanation

To solve by completing the square, first move the constant term to the other side. Then, take half of the coefficient of x, square it, and add it to both sides. Factor the perfect square trinomial and solve for x to get x={±2√17+3}.