(x + 8)2 = 32
(x + 8)2 = 32
2x + 16 = 32
2x = 32 - 16
2x = 16
x = 8
(x+8)2=32
2x+8=32
-8 -8
2x=24
divide each side by 2
x= ?
Ops, Ms. Sue is right actually. I forgot to multiply 8 by 2
To solve the equation (x + 8)² = 32, you can follow these steps:
Step 1: Expand the Square
To eliminate the squared term, you need to expand the expression (x + 8)² using the binomial square formula or by multiplying it by itself:
(x + 8)² = (x + 8)(x + 8)
= x(x) + x(8) + 8(x) + 8(8)
= x² + 8x + 8x + 64
= x² + 16x + 64
So, the equation becomes x² + 16x + 64 = 32.
Step 2: Move the Constant to the Other Side
To isolate the terms with x, subtract 32 from both sides of the equation:
x² + 16x + 64 - 32 = 0
x² + 16x + 32 = 0
Step 3: Solve the Quadratic Equation
Now the equation is in the form ax² + bx + c = 0, where a = 1, b = 16, and c = 32. You can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
Let's solve it by factoring:
x² + 16x + 32 = 0
Factors of 32 that when added or subtracted give 16 are 4 and 8. Rewriting the middle term using these factors:
x² + 4x + 8x + 32 = 0
Group the first two terms and last two terms together:
(x² + 4x) + (8x + 32) = 0
Factor out the common terms from each group:
x(x + 4) + 8(x + 4) = 0
Now, you have a common factor of (x + 4) that you can factor out:
(x + 4)(x + 8) = 0
Now, set each factor equal to zero and solve for x:
x + 4 = 0 or x + 8 = 0
Solving each equation will yield the solutions:
x = -4 or x = -8
So, the solution to the equation (x + 8)² = 32 is x = -4 or x = -8.