Question

Solve the following equation for x: 8x^2 + 6x = -5​

Answer 1

`\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}`

`x=-(3)/(8)+i(√(31))/(8),\:x=-(3)/(8)-i(√(31))/(8)`

Explanation:

`8x^2+6x=-5`

`\mathrm{Add\:}5\mathrm{\:to\:both\:sides}`

`8x^2+6x+5=-5+5`

`8x^2+6x+5=0`

`\underline{\mathrm{Solve\: further\:using\:the\:quadratic\: formula}}`

`x_(1,\:2)=(-6\pm √(6^2-4\cdot \:8\cdot \:5))/(2\cdot \:8)`

`x_(1,\:2)=(-6\pm \:2√(31)i)/(2\cdot \:8)`

`\mathrm{Separate\:the\:solutions}`

`x_1=(-6+2√(31)i)/(2\cdot \:8),\:x_2=(-6-2√(31)i)/(2\cdot \:8)`

`\bold{(-6+2√(31)i)/(2\cdot \:8)=-(3)/(8)+(√(31))/(8)i}`

`\bold{(-6-2√(31)i)/(2\cdot \:8)=-(3)/(8)-(√(31))/(8)i}`

More information

Quadratic equation 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)`