solve for x. (x+2)^2=16
x+2 = + or - 4
x+2 = 4
x = 2
or
x+2 = -4
x = -6
(x+2)^2=16 (x+2)(x+2)=16 x^2+4x-12=16(by expansion).since the equation obtained is a quadratic equation,then factorise the following to obtain x^2+6x-2x-12=0 x(x+6)-2(x+6)=0 x=-6 or x=2
To solve the equation (x + 2)^2 = 16, you'll need to take a few steps:
Step 1: Expand the equation
Expand the left side of the equation using the exponent rule for squaring binomials: (a + b)^2 = a^2 + 2ab + b^2.
(x + 2)^2 = x^2 + 4x + 4
Step 2: Set the expanded equation equal to 16
Now, set the expanded equation equal to 16:
x^2 + 4x + 4 = 16
Step 3: Rearrange the equation
To solve for x, you need to rearrange the equation in the form of a quadratic equation, where one side is equal to zero:
x^2 + 4x + 4 - 16 = 0
x^2 + 4x - 12 = 0
Step 4: Factor or use the quadratic formula
You may try to factor the quadratic equation, but in this case, it won't be possible. Therefore, you can use the quadratic formula to find the solutions.
The quadratic formula is: x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 1, b = 4, and c = -12. Substituting these values into the quadratic formula, we get:
x = (-4 ± √(4^2 - 4(1)(-12))) / (2(1))
x = (-4 ± √(16 + 48)) / 2
x = (-4 ± √64) / 2
x = (-4 ± 8) / 2
Step 5: Solve for x
Now, you have two possible solutions:
x = (-4 + 8) / 2 = 4 / 2 = 2
x = (-4 - 8) / 2 = -12 / 2 = -6
Therefore, the solutions to the equation (x + 2)^2 = 16 are x = 2 and x = -6.