Basic Math Examples

Simplify square root of 10y^2-4y-5=3y
Step 1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2
Simplify each side of the equation.
Tap for more steps...
Step 2.1
Use to rewrite as .
Step 2.2
Simplify the left side.
Tap for more steps...
Step 2.2.1
Simplify .
Tap for more steps...
Step 2.2.1.1
Multiply the exponents in .
Tap for more steps...
Step 2.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.2.1.1.2
Cancel the common factor of .
Tap for more steps...
Step 2.2.1.1.2.1
Cancel the common factor.
Step 2.2.1.1.2.2
Rewrite the expression.
Step 2.2.1.2
Simplify.
Step 2.3
Simplify the right side.
Tap for more steps...
Step 2.3.1
Simplify .
Tap for more steps...
Step 2.3.1.1
Apply the product rule to .
Step 2.3.1.2
Raise to the power of .
Step 3
Solve for .
Tap for more steps...
Step 3.1
Move all terms containing to the left side of the equation.
Tap for more steps...
Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
Subtract from .
Step 3.2
Factor using the AC method.
Tap for more steps...
Step 3.2.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 3.2.2
Write the factored form using these integers.
Step 3.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.4
Set equal to and solve for .
Tap for more steps...
Step 3.4.1
Set equal to .
Step 3.4.2
Add to both sides of the equation.
Step 3.5
Set equal to and solve for .
Tap for more steps...
Step 3.5.1
Set equal to .
Step 3.5.2
Subtract from both sides of the equation.
Step 3.6
The final solution is all the values that make true.
Step 4
Exclude the solutions that do not make true.