# Solve sqrt (x+ a) = x −7 when a=-1

• MHB
• rebo1984
In summary, the conversation discussed the equation sqrt(x+a) = x-7 when a=-1 and identified the unknown variable as x and the value of a as -1. The method for solving the equation was to isolate the square root term and then square both sides, leading to the final solution of x = 3.
rebo1984
Hi,

If a = -1, what is the solution set of the equation sqrt (x+ a) = x −7

{5}
{10}
{5, 10}
No solution(5,10) correct?

Thanks

rebo1984 said:
Hi,

If a = -1, what is the solution set of the equation sqrt (x+ a) = x −7

{5}
{10}
{5, 10}
No solution(5,10) correct?

Thanks

What do you get when you substitute each potential solution into the original equation?

MarkFL said:
What do you get when you substitute each potential solution into the original equation?

It works out.

rebo1984 said:
It works out.

Let's try $$x=5$$:

$$\displaystyle \sqrt{5-1}=5-7$$

$$\displaystyle 2=-2$$

Is this true?

rebo1984 said:
It works out.
What "works out"? Which answer did you get?

## 1. What is the value of x when a is equal to -1?

The value of x is equal to 3 when a is equal to -1.

## 2. How do you solve the equation sqrt (x+ a) = x −7 when a is equal to -1?

To solve this equation, first square both sides to get rid of the square root. This yields x+ a = x^2 - 14x + 49. Then, rearrange the terms to get a quadratic equation in the form of ax^2 + bx + c = 0. In this case, it becomes x^2 - 15x + 49 + a = 0. Finally, use the quadratic formula to solve for x.

## 3. Can this equation be solved using any other method?

Yes, this equation can also be solved using the method of completing the square. This involves manipulating the equation to get it in the form of (x + b/2)^2 = c, where b and c are constants. Then, taking the square root of both sides and solving for x.

## 4. What is the domain and range of this equation?

The domain of this equation is all real numbers except for -a, as it would result in division by zero. The range is also all real numbers, as the square root of any positive number results in a real number.

## 5. Can this equation have multiple solutions?

Yes, this equation can have multiple solutions depending on the value of a. In this case, when a is equal to -1, there are two solutions: x = 3 and x = 7.

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