 Mathematics

### 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? Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service. 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. Wallace H (1013)
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