Solve for X in the Quadratic Equation: x² + 16x + 64 = 81

Video Solution

Solution Steps

00:00 Find X

00:03 Factor 64 into 8 squared

00:11 Factor 16 into 2 and 8

00:20 Use the shortened multiplication formulas to find the brackets

00:25 Extract the root and find the two possible solutions

00:37 Isolate X

00:41 This is one solution

00:47 And this is the second solution

00:50 And this is the solution to the question

Step-by-Step Solution

Let's solve the equation $x^2 + 16x + 64 = 81$ step-by-step:

Step 1: Recognize the Left-Hand Side as a Perfect Square
Notice that the left-hand side, $x^2 + 16x + 64$ , can be factored as $(x + 8)^2$ because $(x + 8)^2 = x^2 + 16x + 64$ .
Step 2: Set the Factored Expression Equal to 81
We have $(x + 8)^2 = 81$ .
Step 3: Take the Square Root of Both Sides
Taking the square root on both sides gives two possible equations: $x + 8 = 9$ and $x + 8 = -9$ .
Step 4: Solve Each Equation
For $x + 8 = 9$ :
Subtract 8 from both sides to get $x = 1$ .
For $x + 8 = -9$ :
Subtract 8 from both sides to get $x = -17$ .

Therefore, the solutions to the equation are $x = -17$ or $x = 1$ .