Question

Solve for k:

47k2+18k=0

If anyone could explain this with steps, it would be a big help to me.
Thank you! :)

Answer 1

`\text{The value of k is } k = 0 \text{ or } k = (-18)/(47)`

Solution:

Given equation is:

`47k^2 +18k = 0`

We can solve the above equation by quadractic formula

`\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}`

`x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)`

`\text{Compare } 47k^2 + 18k = 0 \text{ with } ax^2 + bx + c = 0`

`\mathrm{For\:}\quad a=47,\:b=18,\:c=0:\quad k_(1,\:2)=(-18\pm √(18^2-4\cdot \:47\cdot \:0))/(2\cdot \:47)`

`k=(-18+√(18^2-4\cdot \:47\cdot \:0))/(2\cdot \:47)\\\\\text{Simplify the above expression }\\\\k = (-18 \pm √(324-0))/(94)\\\\k = (-18 \pm √(324))/(94)\\\\k = (-18 \pm 18)/(94)`

Thus we have two solutions:

`k = (-18+18)/(94) \text{ or } k = (-18-18)/(94)\\\\k = 0 \text{ or } k = (-36)/(94)\\\\k = 0 \text{ or } k = (-18)/(47)`

`k = 0 \text{ or } k = (-18)/(47)`

`\text{Thus the value of k is } k = 0 \text{ or } k = (-18)/(47)`