Question
Simplify the expression
Solution
8x−15−x2
Evaluate
5−x×x−3
The product of roots with the same index is equal to the root of the product
(5−x)(x−3)
Solution
More Steps
Evaluate
(5−x)(x−3)
Apply the distributive property
5x−5×3−x×x−(−x×3)
Multiply the numbers
5x−15−x×x−(−x×3)
Multiply the terms
5x−15−x2−(−x×3)
Use the commutative property to reorder the terms
5x−15−x2−(−3x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
5x−15−x2+3x
Add the terms
More Steps
Evaluate
5x+3x
Collect like terms by calculating the sum or difference of their coefficients
(5+3)x
Add the numbers
8x
8x−15−x2
8x−15−x2
Show Solution
Find the roots
Find the roots of the algebra expression
x1=3,x2=5
Evaluate
5−x×x−3
To find the roots of the expression,set the expression equal to 0
5−x×x−3=0
Find the domain
More Steps
Evaluate
{5−x≥0x−3≥0
Calculate
More Steps
Evaluate
5−x≥0
Move the constant to the right side
−x≥0−5
Removing 0 doesn't change the value,so remove it from the expression
−x≥−5
Change the signs on both sides of the inequality and flip the inequality sign
x≤5
{x≤5x−3≥0
Calculate
More Steps
Evaluate
x−3≥0
Move the constant to the right side
x≥0+3
Removing 0 doesn't change the value,so remove it from the expression
x≥3
{x≤5x≥3
Find the intersection
3≤x≤5
5−x×x−3=0,3≤x≤5
Calculate
5−x×x−3=0
Multiply the terms
More Steps
Evaluate
5−x×x−3
The product of roots with the same index is equal to the root of the product
(5−x)(x−3)
Calculate the product
More Steps
Evaluate
(5−x)(x−3)
Apply the distributive property
5x−5×3−x×x−(−x×3)
Multiply the numbers
5x−15−x×x−(−x×3)
Multiply the terms
5x−15−x2−(−x×3)
Use the commutative property to reorder the terms
5x−15−x2−(−3x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
5x−15−x2+3x
Add the terms
8x−15−x2
8x−15−x2
8x−15−x2=0
The only way a root could be 0 is when the radicand equals 0
8x−15−x2=0
Factor the expression
More Steps
Evaluate
8x−15−x2
Reorder the terms
−15+8x−x2
Rewrite the expression
−15+(5+3)x−x2
Calculate
−15+5x+3x−x2
Rewrite the expression
−5×3+5x+x×3−x×x
Factor out −5 from the expression
−5(3−x)+x×3−x×x
Factor out x from the expression
−5(3−x)+x(3−x)
Factor out 3−x from the expression
(−5+x)(3−x)
(−5+x)(3−x)=0
When the product of factors equals 0,at least one factor is 0
−5+x=03−x=0
Solve the equation for x
More Steps
Evaluate
−5+x=0
Move the constant to the right-hand side and change its sign
x=0+5
Removing 0 doesn't change the value,so remove it from the expression
x=5
x=53−x=0
Solve the equation for x
More Steps
Evaluate
3−x=0
Move the constant to the right-hand side and change its sign
−x=0−3
Removing 0 doesn't change the value,so remove it from the expression
−x=−3
Change the signs on both sides of the equation
x=3
x=5x=3
Check if the solution is in the defined range
x=5x=3,3≤x≤5
Find the intersection of the solution and the defined range
x=5x=3
Solution
x1=3,x2=5
Show Solution