Solve the equation for real solutions by using the square root property.
(x+1)^2=64
To solve the equation (x+1)^2=64 using the square root property, we will isolate x and take the square root of both sides of the equation.
First, expand the left side of the equation:
(x+1)(x+1) = 64
x^2 + 2x + 1 = 64
Next, subtract 64 from both sides of the equation to isolate the x terms:
x^2 + 2x + 1 - 64 = 0
x^2 + 2x - 63 = 0
Now, we can use the square root property. Take the square root of both sides of the equation to solve for x:
x + 1 = ±√64
x + 1 = ±8
Next, isolate x by subtracting 1 from both sides of the equation:
x = -1 ± 8
This gives two possible solutions for x:
x = -1 + 8 = 7
x = -1 - 8 = -9
Therefore, the equation (x+1)^2 = 64 has two real solutions, x = 7 and x = -9.
To solve the equation (x+1)^2 = 64 using the square root property, follow these steps:
Step 1: Start with the equation:
(x+1)^2 = 64
Step 2: Apply the square root property, which states that if x^2 = a, then x = ±√a
Taking the square root of both sides, we get:
x + 1 = ±√64
Step 3: Simplify the right side of the equation:
x + 1 = ±8
Step 4: Solve for x:
For the positive square root:
x + 1 = 8
x = 8 - 1
x = 7
For the negative square root:
x + 1 = -8
x = -8 - 1
x = -9
Therefore, the real solutions to the equation (x+1)^2 = 64 are x = 7 and x = -9.
To solve the given equation (x+1)^2 = 64 using the square root property, we can follow these steps:
Step 1: Apply the square root property, which states that if a^2 = b, then a = √b or a = -√b.
Step 2: Take the square root of both sides of the equation, keeping in mind that the square root has two solutions, a positive and a negative:
√((x+1)^2) = √64
Step 3: Simplify the equation by removing the square root and considering both the positive and negative square roots:
x + 1 = ±8
Step 4: Now, solve for x by subtracting 1 from both sides of the equation:
x = -1 ± 8
Step 5: Simplify further by evaluating the positive and negative solutions separately:
x = -1 + 8 = 7
x = -1 - 8 = -9
Therefore, the real solutions to the equation (x+1)^2 = 64 are x = 7 and x = -9.