x^2 - 3 x = 4
x^2 -3 x +(3/2)^2 = 4 + 9/4
(x-1.5)^2 = (1/4)(16 + 9)
(x-1.5)^2 = (1/4)(25) = 25/4
x-3/2 = +/- 5/2
x = 3/2 +/- 5/2
x = 4 or x = -1
Solve by completing the square;round to the nearest hundredth if necessary.
x^2-3x=4
Thanks so much.
4 answers
x ^ 2 - 3 x = 4
The x-term coefficient = − 3
The half of the x-term coefficient = − 3 / 2
After squaring you have ( − 3 / 2 ) ^ 2= 9 / 4
x ^ 2 - 3 x = 4
Add 9 / 4 to both sides
x ^ 2 - 3 x + 9 / 4 = 4 + 9 / 4
x ^ 2 - 3 x + 9 / 4 = 16 / 4 + 9 / 4
x ^ 2 - 3 x + 9 / 4 = 25 / 4
Write the perfect square on the left side:
( x - 3 / 2 ) ^ 2 = 25 / 4
Take the square root of both sides:
x - 3 / 2 = sqroot ( 25 / 4 )
x - 3 / 2 = ± 5 / 2 Add 3 / 2 to both sides
x - 3 / 2 + 3 / 2 = ± 5 / 2 + 3 / 2
x = ± 5 / 2 + 3 / 2
x1 = 5 / 2 + 3 / 2 = 8 / 2 = 4
x2 = - 5 / 2 + 3 / 2 = - 2 / 2 = - 1
The solutions are :
x = - 1 and x = 4
________
Remark:
x ^ 2 - 3 x + 9 / 4 = ( x - 3 / 2 ) ^ 2 becouse:
( x - 3 / 2 ) ^ 2 =
x ^ 2 - 2 * x * 3 / 2 + ( 3 / 2 ) ^ 2 =
x ^ 2 - x * 3 + 9 / 4 =
x ^ 2 - 3 x + 9 / 4
______
The x-term coefficient = − 3
The half of the x-term coefficient = − 3 / 2
After squaring you have ( − 3 / 2 ) ^ 2= 9 / 4
x ^ 2 - 3 x = 4
Add 9 / 4 to both sides
x ^ 2 - 3 x + 9 / 4 = 4 + 9 / 4
x ^ 2 - 3 x + 9 / 4 = 16 / 4 + 9 / 4
x ^ 2 - 3 x + 9 / 4 = 25 / 4
Write the perfect square on the left side:
( x - 3 / 2 ) ^ 2 = 25 / 4
Take the square root of both sides:
x - 3 / 2 = sqroot ( 25 / 4 )
x - 3 / 2 = ± 5 / 2 Add 3 / 2 to both sides
x - 3 / 2 + 3 / 2 = ± 5 / 2 + 3 / 2
x = ± 5 / 2 + 3 / 2
x1 = 5 / 2 + 3 / 2 = 8 / 2 = 4
x2 = - 5 / 2 + 3 / 2 = - 2 / 2 = - 1
The solutions are :
x = - 1 and x = 4
________
Remark:
x ^ 2 - 3 x + 9 / 4 = ( x - 3 / 2 ) ^ 2 becouse:
( x - 3 / 2 ) ^ 2 =
x ^ 2 - 2 * x * 3 / 2 + ( 3 / 2 ) ^ 2 =
x ^ 2 - x * 3 + 9 / 4 =
x ^ 2 - 3 x + 9 / 4
______
1.C
2.C
3.B
4.D
5.B
2.C
3.B
4.D
5.B
answers is correct!!! 100%