Solve by Factoring x^4-10x^2+24=0

Problem

x4−10*x2+24=0

Solution

1. Substitute a new variable to simplify the equation into a quadratic form. Let u=x2

u2−10*u+24=0

2. Factor the quadratic expression by finding two numbers that multiply to 24 and add to −10 These numbers are −6 and −4

(u−6)*(u−4)=0

3. Back-substitute x2 for u to return to the original variable.

(x2−6)*(x2−4)=0

4. Factor further using the difference of squares for the term (x2−4)

(x2−6)*(x−2)*(x+2)=0

5. Set each factor to zero to find the possible values for x

x2−6=0

x−2=0

x+2=0

6. Solve each resulting equation for x

x2=6⇒x=±√(,6)

x=2

x=−2

Final Answer

x=±√(,6),±2

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