SOLUTION: Solve the equation for x: x^2 + 4x + 4 = 7 (x + 2)(x + 2) = 7 (x + 2)^2 = 7 x + 2 = +/- radical 7 x = -2 +/- radical 7 Is this correct?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Solve the equation for x: x^2 + 4x + 4 = 7 (x + 2)(x + 2) = 7 (x + 2)^2 = 7 x + 2 = +/- radical 7 x = -2 +/- radical 7 Is this correct?      Log On


   

Question 89386This question is from textbook Beginning Algebra
: Solve the equation for x:
x^2 + 4x + 4 = 7
(x + 2)(x + 2) = 7
(x + 2)^2 = 7
x + 2 = +/- radical 7
x = -2 +/- radical 7
Is this correct? This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Yes it's correct. You can use other methods such as the quadratic formula to verify your answer.

So let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve x%5E2%2B4%2Ax-3=0 ( notice a=1, b=4, and c=-3)

x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A1%2A-3+%29%29%2F%282%2A1%29 Plug in a=1, b=4, and c=-3



x+=+%28-4+%2B-+sqrt%28+16-4%2A1%2A-3+%29%29%2F%282%2A1%29 Square 4 to get 16



x+=+%28-4+%2B-+sqrt%28+16%2B12+%29%29%2F%282%2A1%29 Multiply -4%2A-3%2A1 to get 12



x+=+%28-4+%2B-+sqrt%28+28+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-4+%2B-+2%2Asqrt%287%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-4+%2B-+2%2Asqrt%287%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-4+%2B+2%2Asqrt%287%29%29%2F2 or x+=+%28-4+-+2%2Asqrt%287%29%29%2F2


Now break up the fraction


x=-4%2F2%2B2%2Asqrt%287%29%2F2 or x=-4%2F2-2%2Asqrt%287%29%2F2


Simplify


x=-2%2Bsqrt%287%29 or x=-2-sqrt%287%29

Notice we get the same answer. So our answer is verified.