Question
Solve the equation
h1=−25,h2=4
Alternative Form
h1=−2.5,h2=4
Evaluate
h10+5=27+h
Find the domain
h10+5=27+h,h=0
Multiply both sides of the equation by LCD
(h10+5)×2h=(27+h)×2h
Simplify the equation
More Steps

Evaluate
(h10+5)×2h
Apply the distributive property
h10×2h+5×2h
Simplify
10×2+5×2h
Multiply the numbers
20+5×2h
Multiply the numbers
20+10h
20+10h=(27+h)×2h
Simplify the equation
More Steps

Evaluate
(27+h)×2h
Apply the distributive property
27×2h+h×2h
Simplify
7h+h×2h
Multiply the terms
More Steps

Evaluate
h×2h
Use the commutative property to reorder the terms
2h×h
Multiply the terms
2h2
7h+2h2
20+10h=7h+2h2
Move the expression to the left side
20+10h−(7h+2h2)=0
Calculate the sum or difference
More Steps

Evaluate
20+10h−(7h+2h2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
20+10h−7h−2h2
Subtract the terms
More Steps

Evaluate
10h−7h
Collect like terms by calculating the sum or difference of their coefficients
(10−7)h
Subtract the numbers
3h
20+3h−2h2
20+3h−2h2=0
Factor the expression
More Steps

Evaluate
20+3h−2h2
Rewrite the expression
20+(8−5)h−2h2
Calculate
20+8h−5h−2h2
Rewrite the expression
4×5+4×2h−h×5−h×2h
Factor out 4 from the expression
4(5+2h)−h×5−h×2h
Factor out −h from the expression
4(5+2h)−h(5+2h)
Factor out 5+2h from the expression
(4−h)(5+2h)
(4−h)(5+2h)=0
When the product of factors equals 0,at least one factor is 0
4−h=05+2h=0
Solve the equation for h
More Steps

Evaluate
4−h=0
Move the constant to the right-hand side and change its sign
−h=0−4
Removing 0 doesn't change the value,so remove it from the expression
−h=−4
Change the signs on both sides of the equation
h=4
h=45+2h=0
Solve the equation for h
More Steps

Evaluate
5+2h=0
Move the constant to the right-hand side and change its sign
2h=0−5
Removing 0 doesn't change the value,so remove it from the expression
2h=−5
Divide both sides
22h=2−5
Divide the numbers
h=2−5
Use b−a=−ba=−ba to rewrite the fraction
h=−25
h=4h=−25
Check if the solution is in the defined range
h=4h=−25,h=0
Find the intersection of the solution and the defined range
h=4h=−25
Solution
h1=−25,h2=4
Alternative Form
h1=−2.5,h2=4
Show Solution
