Question

Vincent is completing his math homework about the process of Completing the Square to solve quadratic equations. His work is shown below.

solve: x²-3x+7=0

step 1: x²-3x = -7
step 2: x²-3x+9=-7 +9
step 3: (x-3)² = 2
step 4: X-3= = √2
x=3 = √2

Did Vincent make a mistake as he solved the quadratic using Completing the Square? If so, in what
step did he first make a mistake? (Step numbers are labeled in blue on the left)

Answer 1

Explanation:

He made a mistake in step one turning the 7 into a -7

`x^(2)` - 3x + 7 = 0

Solving:

`1x^(2)` - 3x + 7 = 0 ← If the term doesn't have a coefficient, it is considered that the coefficient is 1.

`1x^(2)` + (-3x) + 7 = 0 ← Identify the coefficients a, b, and c of the quadratic equation.

a = 1, b = -3, c = 7

x = - (-3) ±√
`(-3)^(2)` - 4 x 1 x 7

2 x 1

x = 3 ± √
`(3)^(2)` - 4 x 7

2

x = 3 ± √9 - 4 x 7

2

x = 3 ±√9 - 28

2

x = 3 ± √-19

2

The square root of a negative number does not exist in the set of real numbers.

x = ∉ R