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

Sep 18th, 2014

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.


Sep 19th, 2014

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