Solve the equation for real solutions by using the square root property.
(x+1)2=64
First, we can rewrite the equation as:
(x + 1)² = 64
To solve for x, we can take the square root of both sides of the equation:
√((x + 1)²) = √64
Simplifying both sides of the equation, we get:
x + 1 = ±8
Now, we can solve for x by subtracting 1 from both sides of the equation:
x = -1 ± 8
Thus, the solutions for x are:
x = -1 + 8 = 7
x = -1 - 8 = -9
To solve the equation (x + 1)² = 64 using the square root property, we need to isolate the squared term first.
1. Expand the equation: (x + 1)(x + 1) = 64
Simplifying, we have: x² + 2x + 1 = 64
2. Subtract 64 from both sides to bring the equation to zero:
x² + 2x + 1 - 64 = 0
x² + 2x - 63 = 0
3. Now, we can apply the square root property. The property states that if x² = a, then x = √a or x = -√a.
4. Rewrite the equation using the square root property:
(x + √63)(x - √63) = 0
5. Solve for x by setting each factor equal to zero:
x + √63 = 0 or x - √63 = 0
6. Solve the first equation:
x + √63 = 0
x = -√63
7. Solve the second equation:
x - √63 = 0
x = √63
Therefore, the real solutions to the equation (x + 1)² = 64 using the square root property are x = -√63 and x = √63.
To solve the equation (x + 1)^2 = 64 using the square root property, we need to isolate the square term and take the square root of both sides of the equation.
Step 1: Expand the equation
(x + 1)^2 = 64
x^2 + 2x + 1 = 64
Step 2: Move the constant term to the other side
x^2 + 2x = 63
Step 3: Apply the square root property
Take the square root of both sides of the equation.
√(x^2 + 2x) = ±√63
Step 4: Simplify the square root on the right side
√(x^2 + 2x) = ±√(9 * 7)
√(x^2 + 2x) = ±√9 * √7
√(x^2 + 2x) = ±3√7
Step 5: Split the equation into two separate equations
To account for both the positive and negative square roots, we need to split the equation.
x + 1 = 3√7 or x + 1 = -3√7
Step 6: Solve each equation for x
Solving the first equation:
x = 3√7 - 1
Solving the second equation:
x = -3√7 - 1
So the real solutions to the equation (x + 1)^2 = 64 are:
x = 3√7 - 1 and x = -3√7 - 1