10 POINTS MATH QUESTIONS?!?!?!?

Question

Transform each equation into a perfect square equation and solve.
1. x^2 + 4x = 5
2. x^2 + 2x = 3
3. t^2 - 8t = -15
4. y^2 - 6y = -5
5. x^2 + 14x = 15
6. 3x^2 - 18x = 21

Answer 1

To solve the eqation, first convert it to a perfect squre eqution and simplfy it. similar process to all given equations.

Recall the formulae ; (a+b)^2 = a^2 + 2ab + b^2

                               (a-b)^2  = a^2- 2ab + b^2

1)x^2 + 4x = 5

x^2 +4x-5 = 0                                                        

x^2+4x +4-9 = 0

(x+2)^2 = 9

x+2 =(+/-) 3

x = 3-2     or    x =-3-2

x = 1        or      x =-5

2)x^2+2x = 3

x^2+2x-3 = 0

x^2+2x+1-4 =0

(x+1)^2-4 = 0

(x+1)^2 = 4

x+1 =(+/-) 2

x = 2-1  or   x = -2-1

x = 1   or      x = -3

3)t^2-8t = -15

t^2 -8t+15 = 0

t^2-8t+16-1 = 0

(t-4)^2 = 1

t-4 =(+/-) 1

t = 1+4        or             t =-1+4

t = 5            or            t = 3

4)y^2-6y = -5               

y^2 -6y+5 = 0

y^2-6y+9-4 = 0

(y-3)^2 = 4

y-3 =(+/-) 2

y = 2+3     or    y = -2+3

y = 5        or    y = 1

5)x^2 +14x = 15

x^2+14x-15 = 0

x^2+14x+49-64 = 0

(x+7)^2 = 64

x+7 =(+/-) 8

x = 8-7    or    x =-8-7

x = 1       or    x = -15

6)3x^2-18x = 21

Apply division property, divide by 3 to each side.

x^2-6x = 7

x^2-6x-7 = 0

x^2-6x+9-16 = 0

(x-3)^2 = 16

x-3 =(+/-) 4

x = 4+3      or     x = -4+3

x = 7         or     x = -1