Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x=6
Evaluate
x2−12=4x
Find the domain
More Steps
Evaluate
{x2−12≥04x≥0
Calculate
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Evaluate
x2−12≥0
Move the constant to the right side
x2≥12
Take the 2-th root on both sides of the inequality
x2≥12
Calculate
∣x∣≥23
Separate the inequality into 2 possible cases
x≥23x≤−23
Find the union
x∈(−∞,−23]∪[23,+∞)
{x∈(−∞,−23]∪[23,+∞)4x≥0
Calculate
{x∈(−∞,−23]∪[23,+∞)x≥0
Find the intersection
x≥23
x2−12=4x,x≥23
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(x2−12)2=(4x)2
Evaluate the power
x2−12=4x
Move the expression to the left side
x2−12−4x=0
Factor the expression
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Evaluate
x2−12−4x
Reorder the terms
x2−4x−12
Rewrite the expression
x2+(2−6)x−12
Calculate
x2+2x−6x−12
Rewrite the expression
x×x+x×2−6x−6×2
Factor out x from the expression
x(x+2)−6x−6×2
Factor out −6 from the expression
x(x+2)−6(x+2)
Factor out x+2 from the expression
(x−6)(x+2)
(x−6)(x+2)=0
When the product of factors equals 0,at least one factor is 0
x−6=0x+2=0
Solve the equation for x
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Evaluate
x−6=0
Move the constant to the right-hand side and change its sign
x=0+6
Removing 0 doesn't change the value,so remove it from the expression
x=6
x=6x+2=0
Solve the equation for x
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Evaluate
x+2=0
Move the constant to the right-hand side and change its sign
x=0−2
Removing 0 doesn't change the value,so remove it from the expression
x=−2
x=6x=−2
Check if the solution is in the defined range
x=6x=−2,x≥23
Find the intersection of the solution and the defined range
x=6
Solution
More Steps
Check the solution
62−12=4×6
Simplify
26=26
Evaluate
true
x=6
Show Solution
Graph
