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Solving the Equation (x+5)^2 = 10
This article will guide you through the process of solving the equation (x+5)^2 = 10.
Understanding the Equation
The equation (x+5)^2 = 10 represents a quadratic equation. It is in the form of a perfect square trinomial, where the left-hand side is a squared binomial.
Solving for x
To solve for x, we need to isolate it. Here are the steps:
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Take the square root of both sides: √(x+5)^2 = ±√10 x + 5 = ±√10
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Isolate x: x = -5 ±√10
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Simplify: x = -5 + √10 or x = -5 - √10
Therefore, the solutions to the equation (x+5)^2 = 10 are x = -5 + √10 and x = -5 - √10.
Verification
We can verify our solutions by plugging them back into the original equation:
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For x = -5 + √10: ((-5 + √10) + 5)^2 = (√10)^2 = 10
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For x = -5 - √10: ((-5 - √10) + 5)^2 = (-√10)^2 = 10
Both solutions satisfy the original equation, confirming their validity.
Conclusion
By using the properties of square roots and simplifying, we successfully solved the quadratic equation (x+5)^2 = 10. The solutions are x = -5 + √10 and x = -5 - √10. Remember, always check your solutions by plugging them back into the original equation to ensure their accuracy.