Question

`x^(2)-5x-24=0`
Quadratic Formula
Please show every step

Answer 1

`x=8,\:x=-3`

Explanation:

`x^2-5x-24=0\\\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)\\\mathrm{For\:}\quad a=1,\:b=-5,\:c=-24:\quad x_(1,\:2)=(-\left(-5\right)\pm √(\left(-5\right)^2-4\cdot \:1\left(-24\right)))/(2\cdot \:1)\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=8,\:x=-3`
`=(5+√(\left(-5\right)^2+4\cdot \:1\cdot \:24))/(2\cdot \:1)\\5+√(\left(-5\right)^2+4\cdot \:1\cdot \:24)\\5+√(121)\\=(5+√(121))/(2)\\=(5+11)/(2)\\=(16)/(2)\\=8\\(-\left(-5\right)-√(\left(-5\right)^2-4\cdot \:1\cdot \left(-24\right)))/(2\cdot \:1)\\=(5-√(\left(-5\right)^2+4\cdot \:1\cdot \:24))/(2\cdot \:1)\\5-√(\left(-5\right)^2+4\cdot \:1\cdot \:24)\\\left(-5\right)^2\\=25\\4\cdot \:1\cdot \:24\\=96\\=5+√(25+96)\\`

`(5-√(121))/(2\cdot \:1)\\(5-11)/(2)\\=-(6)/(2)\\=-3\\`