Question

A)

Huy is solving a quadratic equation by completing the square. His first few steps (steps 1-4) are
shown below. Which of the following statements is true regarding Huy's work?
Given
2² +32-5=0
step 1
Solution
z2 + 3 = 5
step 2
2? + 3x +9 = 5 +9
step 3
(x + 3) = 14
I= -3/14
step 4

Answer 1

This question has errors.

Answer 2

A statement that is true regarding​ Huy's work is: C. Huy is incorrect. He made a mistake in step 2 of the solution when he added a 9 to both sides.

In Mathematics and Euclidean Geometry, the standard form or general form of a quadratic equation is represented by the following equation;

`ax^2 + bx + c = 0`

Next, we would solve the given quadratic equation by using the completing the square method;

`x^2+3x-5=0\\\\x^2+3x=5`

In order to complete the square, we would have to add (half the coefficient of the x-term) squared to both sides of the quadratic equation as follows:

`x^2+3x+((3)/(2) )^2=5+((3)/(2) )^2\\\\x^2+3x+(9)/(4) =5+(9)/(4)\\\\(x+(3)/(2) )^2=(29)/(4) \\\\x=-(3)/(2)\pm \sqrt{(29)/(4)}`

Complete Question:

Huy is solving a quadratic equation by completing the square. His first few steps​ (steps 1-4) are shown below. Which of the following statements is true regarding​ Huy's work?

Given
`x^2+3x-5=0`

Solution
`x^2+3x=5` step 1

`x^2+3x+9=5+9` step 2

`(x+3)^2=14` step 3

`x=-3\pm √(14)` step 4(1 point)

Huy is incorrect. He made a mistake in step 1 when he added a 5 to both sides. He should have only added a 5 to the left side of the equation.

Huy is incorrect. He made a mistake in step 4 when he solved the equation
`(x+3)^2=14` for x.

Huy is incorrect. He made a mistake in step 2 of the solution when he added a 9 to both sides.

Huy is correct. He has done a nice job of completing the square.