Question
23=x+x25+5
Solve the equation
x∈/R
Alternative Form
No real solution
Evaluate
23=x+x25+5
Swap the sides of the equation
x+x25+5=23
Multiply both sides of the equation by LCD
(x+x25+5)×2x=23×2x
Simplify the equation
More Steps

Evaluate
(x+x25+5)×2x
Apply the distributive property
x×2x+x25×2x+5×2x
Simplify
x×2x+25×2+5×2x
Multiply the terms
More Steps

Evaluate
x×2x
Use the commutative property to reorder the terms
2x×x
Multiply the terms
2x2
2x2+25×2+5×2x
Multiply the numbers
2x2+50+5×2x
Multiply the numbers
2x2+50+10x
2x2+50+10x=23×2x
Simplify the equation
2x2+50+10x=3x
Move the expression to the left side
2x2+50+10x−3x=0
Subtract the terms
More Steps

Evaluate
10x−3x
Collect like terms by calculating the sum or difference of their coefficients
(10−3)x
Subtract the numbers
7x
2x2+50+7x=0
Rewrite in standard form
2x2+7x+50=0
Substitute a=2,b=7 and c=50 into the quadratic formula x=2a−b±b2−4ac
x=2×2−7±72−4×2×50
Simplify the expression
x=4−7±72−4×2×50
Simplify the expression
More Steps

Evaluate
72−4×2×50
Multiply the terms
More Steps

Multiply the terms
4×2×50
Multiply the terms
8×50
Multiply the numbers
400
72−400
Evaluate the power
49−400
Subtract the numbers
−351
x=4−7±−351
Solution
x∈/R
Alternative Form
No real solution
Show Solution
