How do you solve #n^2 - 17=64# using the quadratic formula?

Question

Eva Abramson · Accepted Answer

#n=+-9# #n^2-17=64# #n^2=64+17# #n^2=81# #n=sqrt81# #n=+-9#

Nathan Axel · Answer

#n=+-9# Write as #n^2-81# We must apply the quadratic formula, which is expressed as follows: #n^2+0n-81=0# #=>n=(-0+-sqrt(0^2-4(1)(-81)))/(2(1))# #=>n=+-sqrt(324)/2=(+-18)/2 = +-9#

Ethan Adkins · Answer

#n=9, -9#

#n^2-17=64#

Subtract #64# from both sides of the equation.

#n^2-17-64=0#

Simplify.

#n^2-81#

This equation is in the form of a quadratic equation, #ax^2+bx+c=0#, where #a=1#, #b=0#, and #c=-81#.

This quadratic equation can be solved using the quadratic formula.

#x=(-b^2+-sqrt(b^2-4ac))/(2a)#

Substitute #n# for #x# and plug the known values into the formula.

#n=(-0+-sqrt(0^2-4*1*-81))/(2*1)#

Simplify.

#n=(+-sqrt(324))/(2)#

Simplify.

#n=+-18/2#

Simplify.

#n=+-9#

Solve for #n#.

#n=9#

#n=-9#

Isaiah Anthony · Answer

undefined To solve the equation $n^2 - 17 = 64$ using the quadratic formula, first, rewrite the equation in the form $ax^2 + bx + c = 0$, where $a = 1$, $b = 0$, and $c = -81$. Then, plug these values into the quadratic formula: $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$.

Substitute the values into the formula: $n = \frac{{-0 \pm \sqrt{{0^2 - 4(1)(-81)}}}}{{2(1)}}$.

Simplify inside the square root: $n = \frac{{\pm \sqrt{{324}}}}{{2}}$.

Calculate the square root: $n = \frac{{\pm 18}}{{2}}$.

Simplify further: $n = \pm 9$.

So, the solutions to the equation $n^2 - 17 = 64$ are $n = 9$ and $n = -9$.

Julia Adams · Answer

undefined To solve the equation $ n^2 - 17 = 64 $ using the quadratic formula, follow these steps:

1. Identify the coefficients $ a $, $ b $, and $ c $ in the quadratic equation $ ax^2 + bx + c = 0 $.
   - Here, $ a = 1 $, $ b = 0 $, and $ c = -81 $ (since $ 17 - 64 = -81 $).

2. Substitute the values of $ a $, $ b $, and $ c $ into the quadratic formula:
   $$ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} $$

3. Plug in the values:
   $$ n = \frac{{-0 \pm \sqrt{{0^2 - 4 \cdot 1 \cdot (-81)}}}}{{2 \cdot 1}} $$

4. Simplify the expression inside the square root:
   $$ n = \frac{{\pm \sqrt{{324}}}}{2} $$

5. Find the square root:
   $$ n = \frac{{\pm 18}}{2} $$

6. Simplify further:
   $$ n = \frac{{18}}{2} \quad \text{or} \quad n = \frac{{-18}}{2} $$

7. Reduce the fractions:
   $$ n = 9 \quad \text{or} \quad n = -9 $$

So, the solutions to the equation $ n^2 - 17 = 64 $ are $ n = 9 $ and $ n = -9 $.