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View this equation as a quadratic like so: [tex]x^2(x^2)-13x(x)+36=0[/tex]
We can factor just like a normal quadartic! We want two numbers that multiply to 36x² and add to -13x. These numbers are -9x and -4x. Because our leading coefficient is 1, we can factor straight to (x²-4)(x²-9). Here's what it would look like if we split the middle and factored: [tex]x^4-9x^2-4x^2+36=0\\x^2(x^2-9)-4(x^2-9)=0\\(x^2-4)(x^2-9)=0[/tex]
Of course, any value which causes either factor to equal zero is a solution. The other factor times zero is still going to be zero, of course. Let's derive these two possibilities from our equation. [tex]x^2-4=0,\ or\ x^2-9=0[/tex] We can add that constant to the right side... [tex]x^2=4,\ or\ x^2=9[/tex] And take the square root of each side. [tex]\boxed{x=\pm2\ or\ \pm3}[/tex]
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