How do you solve #sqrt(x+15)  sqrt(2x+7)=1#?
Even before doing any calculations, you know that any possible solution to this equation must satisfy two conditions
These condtions are required because you can't take the square root of a negative number if you're working with real numbers.
In other words, you can only take the square root of positive real numbers; likewise, taking the square root of a positive number will always result in a positive number.
Start by squaring both sides of the equation; this will reduce the number of radical terms from two to one
Isolate the remaining radical term on one side of the equation
Once again, square both sides of the equation to get rid of the radical lterm
Rearrange this equation to classic quadratic form
You can use the quadratic equation to find the two roots of this quadratic equation
More specifically,
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To solve the equation sqrt(x+15)  sqrt(2x+7) = 1, you can follow these steps:

Start by isolating one of the square root terms on one side of the equation. Let's isolate sqrt(x+15) by adding sqrt(2x+7) to both sides: sqrt(x+15) = sqrt(2x+7) + 1

Square both sides of the equation to eliminate the square roots: (sqrt(x+15))^2 = (sqrt(2x+7) + 1)^2

Simplify the equation: x + 15 = (sqrt(2x+7) + 1)^2

Expand the right side of the equation: x + 15 = (sqrt(2x+7))^2 + 2(sqrt(2x+7)) + 1

Simplify further: x + 15 = 2x + 7 + 2(sqrt(2x+7)) + 1

Combine like terms: x + 15 = 2x + 8 + 2(sqrt(2x+7))

Move all terms involving x to one side of the equation and all constant terms to the other side: x  2x = 8 + 2(sqrt(2x+7))  15

Simplify: x = 7 + 2(sqrt(2x+7))

Multiply both sides by 1 to eliminate the negative sign: x = 7  2(sqrt(2x+7))

Square both sides of the equation to eliminate the square root: x^2 = (7  2(sqrt(2x+7)))^2

Expand the right side of the equation: x^2 = 49  28(sqrt(2x+7)) + 4(2x+7)

Simplify further: x^2 = 49  28(sqrt(2x+7)) + 8x + 28

Combine like terms: x^2  8x  77 = 28(sqrt(2x+7))

Square both sides of the equation again: (x^2  8x  77)^2 = (28(sqrt(2x+7)))^2

Expand both sides of the equation: x^4  16x^3 + 161x^2 + 1232x + 5929 = 784(2x+7)

Simplify further: x^4  16x^3 + 161x^2 + 1232x + 5929 = 1568x + 5496

Rearrange the equation to bring all terms to one side: x^4  16x^3 + 161x^2 + 1232x  1568x  5496 + 5929 = 0

Combine like terms: x^4  16x^3 + 161x^2 + 664x + 431 = 0

At this point, the equation cannot be easily solved algebraically. You may need to use numerical methods or a graphing calculator to approximate the solutions.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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