%5E2%3D100.jpeg "(x+5)^2=100")
Solving the Equation (x+5)^2 = 100
This equation involves a squared term, so we'll need to use the square root property to solve for x.
Here's the step-by-step solution:
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Take the square root of both sides: √[(x+5)^2] = ±√100
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Simplify: x + 5 = ±10
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Isolate x by subtracting 5 from both sides: x = -5 ± 10
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Solve for the two possible values of x:
- x = -5 + 10 = 5
- x = -5 - 10 = -15
Therefore, the solutions to the equation (x+5)^2 = 100 are x = 5 and x = -15.
Explanation:
The square root of a number can be either positive or negative. This is why we have the "±" symbol in step 2. We need to consider both possibilities when solving for x.
Checking our answers:
Let's substitute the solutions back into the original equation to verify they are correct:
- For x = 5: (5 + 5)^2 = 10^2 = 100
- For x = -15: (-15 + 5)^2 = (-10)^2 = 100
Both solutions satisfy the original equation.