### Question Description

I don’t understand this Mathematics question and need help to study.

the difference between the solutions to the equation x squared = a is 30. what is a?

## Final Answer

I am assuming that 'x' and 'a' are the variables we are using for the solutions.

The equation representing the difference between both solutions would probably be:

a - x = 30

Since we are given that x^2 = a, that means that a = x^2. And we can substitute into the equation and then solve for x.

*a - x = 30 <Difference Equation>*

* x^2 - x = 30* *<Since a = x^2, we can replace a with x^2>*

* Equation is now quadratic, so we can solve for x*

* x^2 - x - 30 = 30 - 30 <Subtract both sides by 30>*

* x^2 - x - 30 = 0*

* (x + 5)(x - 6) = 0 <Left side is factored>*

* x + 5 = 0 or x - 6 = 0* *<Zero Product Property>*

* x + 5 - 5 = 0 - 5 or x - 6 + 6 = 0 + 6 <Solve each equation separately>*

* x = -5 or x = 6*

* I am thinking we need to use the positive x-value, so we can try x = 6*

Now that we have our value of x, we can substitute back into our difference equation to solve for 'a'

*a - x = 30 <Difference Equation>*

* a - 6 = 30 <Substituting our calculated value of x, which is x = 6>*

* a - 6 + 6 = 30 + 6 <Add both sides by 6>*

* a = 36*

**POSSIBLE SOLUTION: a = 36 (Only if you are required to use just the positive x value)**

I don't know if your problem requires more than one answer. But just in case, we will also test x = -5

*a - x = 30 <Difference Equation>*

* a - (-5) = 30 <Substitute x = -5>*

* a + 5 = 30 < A - (-B) is the same as A + B>*

* a + 5 - 5 = 30 - 5 <Subtract both sides by 5>*

* a = 25*

**POSSIBLE SOLUTION: a = 36 or a = 25 (Only if you needed more than one solution)**

I hope this helps.

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors