How do you solve #x^2 +10x = 4# by completing the square?
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To solve the equation x^2 + 10x = 4 by completing the square, follow these steps:
- Move the constant term to the other side of the equation: x^2 + 10x - 4 = 0.
- Add and subtract the square of half the coefficient of x (the middle term): x^2 + 10x + (10/2)^2 - (10/2)^2 - 4 = 0.
- Simplify: x^2 + 10x + 25 - 25 - 4 = 0.
- Combine like terms: x^2 + 10x + 21 = 0.
- Rewrite as a perfect square trinomial: (x + 5)^2 - 4 = 0.
- Add 4 to both sides: (x + 5)^2 = 4.
- Take the square root of both sides: x + 5 = ±√4.
- Solve for x: x + 5 = ±2.
- Subtract 5 from both sides: x = -5 ± 2.
Therefore, the solutions are x = -5 + 2 and x = -5 - 2, which simplify to x = -3 and x = -7.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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