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(a+5)^2=64: Solving the Equation
In this article, we will explore the solution to the equation (a+5)^2=64.
What does the equation mean?
The equation (a+5)^2=64 is a quadratic equation where a is the variable, and 5 is a constant. The equation is saying that the square of the expression (a+5) is equal to 64.
Expanding the Equation
To solve the equation, we need to expand the expression (a+5)^2 using the formula for the square of a binomial:
(a+5)^2 = (a+5)(a+5)
= a^2 + 10a + 25
Now, we can equate this expanded expression to 64:
a^2 + 10a + 25 = 64
Solving the Equation
To solve for a, we can subtract 25 from both sides of the equation:
a^2 + 10a = 39
Next, we can try to factor the left-hand side:
(a + 13)(a - 3) = 0
This tells us that either (a + 13) = 0 or (a - 3) = 0.
Solving for a, we get:
a + 13 = 0 --> a = -13
a - 3 = 0 --> a = 3
Therefore, the solutions to the equation (a+5)^2=64 are a = -13 and a = 3.
Conclusion
In this article, we have solved the equation (a+5)^2=64 and found that the solutions are a = -13 and a = 3. This equation is a simple example of a quadratic equation, and by expanding the expression and solving for a, we can find the solutions.
