Question

What are the solutions to the equation x^4+95x^2-500=0

Answer 1

Answer: x=2.23606797749979 or x=−2.23606797749979

Explanation:

Answer 2

Answer by Mimiwhatsup:

`\mathrm{Rewrite\:the\:equation\:with\:}u=x^2\mathrm{\:and\:}u^2=x^4\\u^2+95u-500=0\\\mathrm{Solve\:}\:u^2+95u-500=0\\Solve\:with\:the\:quadratic\: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)\\\mathrm{For\:}\quad a=1,\:b=95,\:c=-500:\quad u_(1,\:2)=(-95\pm √(95^2-4\cdot \:1\left(-500\right)))/(2\cdot \:1)\\(-95+√(95^2-4\cdot \:1\cdot \left(-500\right)))/(2\cdot \:1)\\`

`\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=(-95+√(95^2+4\cdot \:1\cdot \:500))/(2\cdot \:1)\\√(95^2+4\cdot \:1\cdot \:500)\\95^2=9025\\=√(9025+4\cdot \:1\cdot \:500)\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:1\cdot \:500=2000\\=√(9025+2000)\\\mathrm{Add\:the\:numbers:}\:9025+2000=11025\\=√(11025)\\=(-95+105)/(2)\\\mathrm{Add/Subtract\:the\:numbers:}\:-95+105=10\\=(10)/(2)\\\mathrm{Divide\:the\:numbers:}\:(10)/(2)=5\\`

`u=(-95-√(95^2-4\cdot \:1\left(-500\right)))/(2\cdot \:1):\quad -100\\\mathrm{The\:final\:solutions\:to\:the\:quadratic\:equation\:are:}\\u=5,\:u=-100\\\mathrm{Since\:}u=x^2\mathrm{,\:solve\:the\:following\:equations\:in\:order\:to\:find\:}\\\mathrm{Solve\:}\:x^2=5:\quad x=√(5),\:x=-√(5)\\\mathrm{Solve\:}\:x^2=-100:\quad x=10i,\:x=-10i\\\mathrm{The\:final\:solutions\:to\:the\:equation\:are:}\\x=√(5),\:x=-√(5),\:x=10i,\:x=-10i`