Question

Consider the equation: 24=x^2-4x+324=x 2 −4x+324, equals, x, squared, minus, 4, x, plus, 3 1) Rewrite the equation by completing the square. Your equation should look like (x+c)^2=d(x+c) 2 =dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or (x-c)^2=d(x−c) 2 =dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d. 2) What are the solutions to the equation? Choose 1 answer:

Answer 1

Answer:

a) (x-2)² = 25

b) 7 and -3

Step-by-step explanation:

Given the expression 24 = x^2 - 4x + 3

Rewrite

x^2 - 4x + 3 - 24  = 0

x^2 - 4x - 21 = 0

Add 21 to both sides

x^2 - 4x - 21 + 21 = 0 + 21

x^2 - 4x = 21

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

constant to add = (-4/2)² = (-2)²

x^2 - 4x + (-2)²  = 21 + (-2)²

(x-2)² = 21 + 4

(x-2)² = 25

Hence the rewritten form of the equation is (x-2)² = 25

Calculate the value of x

(x-2)² = 25

Square root both sides

√(x-2)² = ±√25

x - 2 = ±5

x= ±5 + 2

x = 5 +2 and-5+2

x = 7 and -3

Hence the solutions to the equation are 7 and -3