Question

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solve this quadratic equation:
please solve it with step by step explanation...

${e}^{2} \: - \: 16e \: + \: 64 = 0$



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Answer 1

Equation :-

• e² - 16e + 64 = 0

Answer :-

• e = {8,8}

Explanation :-

given equation

$\rm :\longmapsto\:e^{2} + 16e + 64 = 0$

by reorder the terms

$\rm :\longmapsto\:64 + - 16e + {6}^{2} = 0$

by solving

$\rm :\longmapsto\:64 + - 16 + {6}^{2} = 0$

by solving for variable 'e'

factor a trinomial

$\rm :\longmapsto\:(8 + - 1e)(8 + 1e) = 0$

problem 1 :-

set the factor (8 + -1e) equal to zero and attempt to solve

simplifying :-

$\rm :\longmapsto\:8 + - 1e = 0$

solving

$\rm :\longmapsto\: 8 + - 1e = 0$

now move the all terms containing e to the left , all other terms to the right

now add -8 to each side of the equation

$\rm :\longmapsto\:8 + - 8 + - 1e = 0 + - 8$

by combine like terms

$\rm :\longmapsto\:0 + - 8 = - 8 - 1e = - 8 \\ \\ \rm :\longmapsto\:1e = 0 + 8$

again by combining like terms

$\rm :\longmapsto\:0 + - 8 = - 8 - 1e = - 8$

divide each side by '1' so we get,

$\rm :\longmapsto\:e = 8$

simlifying :- e = 8

problem 2 :-

set the factor (8 + -1e) equal to zero and attempt to solve

simplifying

$\rm :\longmapsto\:8 + - 1e = 0$

solving

$\rm :\longmapsto\:8 + - 1e = 0$

now move all terms containing e to the left all other terms to the right

now add -8 to each side of the equation

$\rm :\longmapsto\:8 + - 8 + - 1e = 0 + 8$

now by combining like terms

$\rm :\longmapsto\:0 + - 8 = - 8 - 1e = - 8 \\ \\ \rm :\longmapsto\:1e = 0 + 8$

now again by combining like terms

$\rm :\longmapsto\:0 + - 8 = - 8 - 1e = - 8$

divide each side by -1

$\rm :\longmapsto\:e = 8$

simlifying : e = 8

so therefore our required answer is e = {8,8}