Algebra
Calculus
Trigonometry
Matrix
Question
(3x)2−22x−23
Simplify the expression
3x−22x−23
Evaluate
(3x)2−22x−23
Solution
More Steps
Calculate
(3x)2
Rewrite the expression
3x×3x
When a square root of an expression is multiplied by itself,the result is that expression
3x
3x−22x−23
Show Solution
Find the roots
x=94+63+41+33
Alternative Form
x≈2.705459
Evaluate
(3x)2−22x−23
To find the roots of the expression,set the expression equal to 0
(3x)2−22x−23=0
Find the domain
More Steps
Evaluate
{3x≥02x≥0
Calculate
{x≥02x≥0
Calculate
{x≥0x≥0
Find the intersection
x≥0
(3x)2−22x−23=0,x≥0
Calculate
(3x)2−22x−23=0
Rewrite the expression
More Steps
Simplify
(3x)2−22x
Rewrite the expression
More Steps
Calculate
(3x)2
Rewrite the expression
3x×3x
When a square root of an expression is multiplied by itself,the result is that expression
3x
3x−22x
3x−22x−23=0
Move the expression to the right-hand side and change its sign
−22x=−3x+23
Rewrite the expression
2x=23x−23
Evaluate
2x=23x−23,23x−23≥0
Evaluate
More Steps
Evaluate
23x−23≥0
Simplify
3x−23≥0
Move the constant to the right side
3x≥0+23
Removing 0 doesn't change the value,so remove it from the expression
3x≥23
Divide both sides
33x≥323
Divide the numbers
x≥323
2x=23x−23,x≥323
Solve the equation for x
More Steps
Evaluate
2x=23x−23
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(2x)2=(23x−23)2
Evaluate the power
2x=49x2−123×x+12
Cross multiply
2x×4=9x2−123×x+12
Simplify the equation
8x=9x2−123×x+12
Move the expression to the left side
8x−(9x2−123×x+12)=0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
8x−9x2+123×x−12=0
Collect like terms by calculating the sum or difference of their coefficients
(8+123)x−9x2−12=0
Rewrite in standard form
−9x2+(8+123)x−12=0
Multiply both sides
9x2+(−8−123)x+12=0
Substitute a=9,b=−8−123 and c=12 into the quadratic formula x=2a−b±b2−4ac
x=2×98+123±(−8−123)2−4×9×12
Simplify the expression
x=188+123±(−8−123)2−4×9×12
Simplify the expression
More Steps
Evaluate
(−8−123)2−4×9×12
Multiply the terms
(−8−123)2−432
Rewrite the expression
(8+123)2−432
Evaluate the power
496+1923−432
Subtract the numbers
64+1923
x=188+123±64+1923
Simplify the radical expression
More Steps
Evaluate
64+1923
Factor the expression
64(1+33)
The root of a product is equal to the product of the roots of each factor
64×1+33
Evaluate the root
81+33
x=188+123±81+33
Separate the equation into 2 possible cases
x=188+123+81+33x=188+123−81+33
Simplify the expression
x=94+63+41+33x=188+123−81+33
Simplify the expression
x=94+63+41+33x=94+63−41+33
x=94+63+41+33x=94+63−41+33,x≥323
Find the intersection
x=94+63+41+33
Check if the solution is in the defined range
x=94+63+41+33,x≥0
Solution
x=94+63+41+33
Alternative Form
x≈2.705459
Show Solution