Question
Find the roots
x1=955778−33427790,x2=955778+33427790
Alternative Form
x1≈11.009779,x2≈12384.101332
Evaluate
3x−334x−11
To find the roots of the expression,set the expression equal to 0
3x−334x−11=0
Find the domain
More Steps

Evaluate
x−11≥0
Move the constant to the right side
x≥0+11
Removing 0 doesn't change the value,so remove it from the expression
x≥11
3x−334x−11=0,x≥11
Calculate
3x−334x−11=0
Move the expression to the right-hand side and change its sign
−334x−11=−3x
Divide both sides of the equation by −1
334x−11=3x
Rewrite the expression
x−11=3343x
Evaluate
x−11=3343x,3343x≥0
Evaluate
More Steps

Evaluate
3343x≥0
Simplify
3x≥0
Rewrite the expression
x≥0
x−11=3343x,x≥0
Solve the equation for x
More Steps

Evaluate
x−11=3343x
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(x−11)2=(3343x)2
Evaluate the power
x−11=33429x2
Multiply both sides of the equation by LCD
(x−11)×3342=33429x2×3342
Simplify the equation
More Steps

Evaluate
(x−11)×3342
Apply the distributive property
x×3342−11×3342
Use the commutative property to reorder the terms
3342x−11×3342
3342x−11×3342=33429x2×3342
Simplify the equation
3342x−11×3342=9x2
Move the expression to the left side
3342x−11×3342−9x2=0
Rewrite in standard form
−9x2+3342x−11×3342=0
Multiply both sides
9x2−3342x+11×3342=0
Substitute a=9,b=−3342 and c=11×3342 into the quadratic formula x=2a−b±b2−4ac
x=2×93342±(−3342)2−4×9×11×3342
Simplify the expression
x=183342±(−3342)2−4×9×11×3342
Simplify the expression
More Steps

Evaluate
(−3342)2−4×9×11×3342
Multiply the terms
(−3342)2−396×3342
Calculate
(3342)2−396×3342
Multiply the exponents
3344−396×3342
Rewrite the expression
27889×4×3342−99×4×3342
Factor the expression
(27889−99)×4×3342
Subtract the terms
27790×4×3342
Multiply the terms
111160×3342
x=183342±111160×3342
Simplify the radical expression
More Steps

Evaluate
111160×3342
Rewrite the expression
111160×3342
Simplify the root
66827790
x=183342±66827790
Separate the equation into 2 possible cases
x=183342+66827790x=183342−66827790
Simplify the expression
x=955778+33427790x=183342−66827790
Simplify the expression
x=955778+33427790x=955778−33427790
x=955778+33427790x=955778−33427790,x≥0
Find the intersection
x=955778+33427790x=955778−33427790
Check if the solution is in the defined range
x=955778+33427790x=955778−33427790,x≥11
Find the intersection of the solution and the defined range
x=955778+33427790x=955778−33427790
Solution
x1=955778−33427790,x2=955778+33427790
Alternative Form
x1≈11.009779,x2≈12384.101332
Show Solution
