Question

Please help me so confused Solve. x^2 + 3x − 7 = 0 Enter your answers, as exact values, in the boxes. x = or x =

Answer 1

-1.5 -√9.25 or -1.5 +√9.25

Explanation:

x^2 + 3x - 7 = 0

This will not factor so we can use completing the square:

x^2 + 3x = 7

(x + 1.5)^2 - 2.25 = 7

(x + 1.5)^2 = 9.25

x + 1.5 = ±√9.25

x = -1.5 ±√9.25

Answer 2

x = -1/2 ( 3±sqrt(37))

Explanation:

x^2 + 3x − 7 = 0

Add 7 to each side

x^2 + 3x =7

Using complete the square

Taking the coefficient of x

3

Divide by 2

3/2

Square it

(3/2)^2 = 9/4

Add this to each side

x^2 + 3x+ 9/4 = 7+9/4

( x+ 3/2) ^2 = 28/4 + 9/4

( x+ 3/2) ^2 = 37/4

Take the square root of each side

x+3/2 = ±sqrt(37/4)

x+3/2 = ±sqrt(37) / sqrt(4)

x+ 3/2 = ±sqrt(37) / 2

Subtract 3/2 from each side

x = -3/2 ±sqrt(37) / 2

x = -1/2 ( 3±sqrt(37))