How do you solve #x^2=24x+10# by completing the square?
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To solve the equation ( x^2 = 24x + 10 ) by completing the square, follow these steps:
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Move the constant term to the other side of the equation: [ x^2 - 24x = 10 ]
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Take half of the coefficient of the x-term (-24), square it, and add it to both sides of the equation: [ x^2 - 24x + (-24/2)^2 = 10 + (-24/2)^2 ] [ x^2 - 24x + 144 = 10 + 144 ]
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Simplify the equation: [ x^2 - 24x + 144 = 154 ]
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Write the left side of the equation as a perfect square: [ (x - 12)^2 = 154 ]
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Take the square root of both sides and solve for x: [ x - 12 = \pm \sqrt{154} ] [ x = 12 \pm \sqrt{154} ]
Therefore, the solutions to the equation ( x^2 = 24x + 10 ) by completing the square are: [ x = 12 + \sqrt{154} ] and ( x = 12 - \sqrt{154} ).
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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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