Question

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

Answer 1

Answer: x=2.23606797749979 or x=−2.23606797749979

Step-by-step explanation:

Answer 2

Answer by Mimiwhatsup:

$\mathrm{Rewrite\:the\:equation\:with\:}u=x^2\mathrm{\:and\:}u^2=x^4\\u^2+95u-500=0\\\mathrm{Solve\:}\:u^2+95u-500=0\\Solve\:with\:the\:quadratic\:formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=95,\:c=-500:\quad u_{1,\:2}=\frac{-95\pm \sqrt{95^2-4\cdot \:1\left(-500\right)}}{2\cdot \:1}\\\frac{-95+\sqrt{95^2-4\cdot \:1\cdot \left(-500\right)}}{2\cdot \:1}$

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

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