Question

Lucas and Tony were trying to solve the equation: x^2=16x+25 Lucas said, “The x^2 squared term is isolated, so I"ll take the square root of both sides and solve.” Tony said, “I'll solve using the quadratic formula with a=1a=1a, equals, 1, b=16 Whose solution strategy would work?

Answer 1

Answer:

Neither

Step-by-step explanation:

I used the cancellation method i guessed till i got it right

Answer 2

Given: The given equation is $x^{2} = 16x +25$.

Lucas use square roots to solve the equation.

Tony use quadratic formula to solve the equation.

Find: Whose solution strategy will work?

Solution: $x^{2} =16x + 25$

Method 1 : Taking square root on both sides

                  $\sqrt{x^{2} } =\sqrt{16x+25}$

               = $x = \sqrt{(4x)^{2}+(5)^{2} }$

Method 2 : By quadratic formula

                 $x^{2} = 16x +25$

             = $x^{2} - 16x -25 = 0$

             Now,

              D = $b^{2} - 4ac = (16)^{2} -4.1.25 = 256-100 = 156$

              $\sqrt{D} = 2\sqrt{39}$

            $\alpha =\frac{-b+\sqrt{D} }{2a}$

            $\alpha = \frac{16+2\sqrt{39} }{2} = 4+\sqrt{39}$

            And

             $\beta = \frac{-b-\sqrt{D} }{2}$

             $\beta = \frac{16-2\sqrt{39} }{2} = 4 - \sqrt{39}$

Therefore, with the help of Tony's method we can find the roots of the equation.

Hence, Tony solution strategy would work.

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