Give step by step to solve this equation 2(x-3)²-32=0

Please Follow through my step-by-step tutorial till the end:

1.) First, move the number(s) to the other side. (algebra rules)

2(x-3)²-32+32=0+32

2(x-3)² = 32

2.) Next, divide every term by 2 to factor out the 2.

2(x-3)²/2 = 32/2

(x-3)² = 16

3.) Third, square root both sides (algebraic rules)

4.) Since the square root of 16 is both +4 and -4, we will have two answers. Next we split the equation in two forms.

(x-3) = 4                (x-3) = -4

x-3+3 = 4+3          x-3+3 = -4+3

x=7                        x=-1

5.) So we get two answers x= 7 and x= -1

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3