To calculate: The solution of the equation x2−5=(x+2)(x−4).

Question

inenge3y · Accepted Answer

Formula used:
The distributive property is

a (b + c) = a b + a c

.
Calculation:
Consider the equation

x^{2} - 5 = (x + 2) (x - 4)

.
Apply the distributive property.

x^{2} - 5 = x^{2} - 4 x + 2 x - 8

x^{2} - 5 = x^{2} - 2 x - 8

- 5 = - 2 x - 8

8 - 5 = - 2 x

Further solve the equation.

3 = - 2 x

x = - \frac{3}{2}

Check the solution

x = - \frac{3}{2}

in the equation

x^{2} - 5 = (x + 2) (x - 4)

.

{(- \frac{3}{2})}^{2} - 5 \overset{?}{=} {(- \frac{3}{2}) + 2} {(- \frac{3}{2}) - 4}

\frac{9}{4} - 5 \overset{?}{=} (\frac{- 3 + 4}{2}) (\frac{- 3 - 8}{2})

\frac{9 - 20}{4} \overset{?}{=} (\frac{1}{2}) (- \frac{11}{2})

- \frac{11}{4} = - \frac{11}{4}

Thus, this solution is true.
Therefore, thesolution of the equation

x^{2} - 5 = (x + 2) (x - 4)

is

{3}

.

To calculate: The solution of the equation x^{2}-5=\left(x+2\right)