Finite Math Examples

Find the Equation with Real Coefficients 0.3x+0.3x^2+0.8x^3=0 , 0.5x+0.6x^2=0 , 0.2x+0.1x^2+0.2x^3=0
, ,
Step 1
Factor out of .
Tap for more steps...
Step 1.1
Factor out of .
Step 1.2
Factor out of .
Step 1.3
Factor out of .
Step 1.4
Factor out of .
Step 1.5
Factor out of .
Step 2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3
Set equal to .
Step 4
Set equal to and solve for .
Tap for more steps...
Step 4.1
Set equal to .
Step 4.2
Solve for .
Tap for more steps...
Step 4.2.1
Use the quadratic formula to find the solutions.
Step 4.2.2
Substitute the values , , and into the quadratic formula and solve for .
Step 4.2.3
Simplify.
Tap for more steps...
Step 4.2.3.1
Simplify the numerator.
Tap for more steps...
Step 4.2.3.1.1
Raise to the power of .
Step 4.2.3.1.2
Multiply .
Tap for more steps...
Step 4.2.3.1.2.1
Multiply by .
Step 4.2.3.1.2.2
Multiply by .
Step 4.2.3.1.3
Subtract from .
Step 4.2.3.1.4
Rewrite as .
Step 4.2.3.1.5
Rewrite as .
Step 4.2.3.1.6
Rewrite as .
Step 4.2.3.2
Multiply by .
Step 4.2.4
Simplify the expression to solve for the portion of the .
Tap for more steps...
Step 4.2.4.1
Simplify the numerator.
Tap for more steps...
Step 4.2.4.1.1
Raise to the power of .
Step 4.2.4.1.2
Multiply .
Tap for more steps...
Step 4.2.4.1.2.1
Multiply by .
Step 4.2.4.1.2.2
Multiply by .
Step 4.2.4.1.3
Subtract from .
Step 4.2.4.1.4
Rewrite as .
Step 4.2.4.1.5
Rewrite as .
Step 4.2.4.1.6
Rewrite as .
Step 4.2.4.2
Multiply by .
Step 4.2.4.3
Change the to .
Step 4.2.4.4
Rewrite as .
Step 4.2.4.5
Factor out of .
Step 4.2.4.6
Factor out of .
Step 4.2.4.7
Move the negative in front of the fraction.
Step 4.2.5
Simplify the expression to solve for the portion of the .
Tap for more steps...
Step 4.2.5.1
Simplify the numerator.
Tap for more steps...
Step 4.2.5.1.1
Raise to the power of .
Step 4.2.5.1.2
Multiply .
Tap for more steps...
Step 4.2.5.1.2.1
Multiply by .
Step 4.2.5.1.2.2
Multiply by .
Step 4.2.5.1.3
Subtract from .
Step 4.2.5.1.4
Rewrite as .
Step 4.2.5.1.5
Rewrite as .
Step 4.2.5.1.6
Rewrite as .
Step 4.2.5.2
Multiply by .
Step 4.2.5.3
Change the to .
Step 4.2.5.4
Rewrite as .
Step 4.2.5.5
Factor out of .
Step 4.2.5.6
Factor out of .
Step 4.2.5.7
Move the negative in front of the fraction.
Step 4.2.6
The final answer is the combination of both solutions.
Step 5
The final solution is all the values that make true.
Step 6
Factor out of .
Tap for more steps...
Step 6.1
Factor out of .
Step 6.2
Factor out of .
Step 6.3
Factor out of .
Step 7
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 8
Set equal to .
Step 9
Set equal to and solve for .
Tap for more steps...
Step 9.1
Set equal to .
Step 9.2
Solve for .
Tap for more steps...
Step 9.2.1
Subtract from both sides of the equation.
Step 9.2.2
Divide each term in by and simplify.
Tap for more steps...
Step 9.2.2.1
Divide each term in by .
Step 9.2.2.2
Simplify the left side.
Tap for more steps...
Step 9.2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 9.2.2.2.1.1
Cancel the common factor.
Step 9.2.2.2.1.2
Divide by .
Step 9.2.2.3
Simplify the right side.
Tap for more steps...
Step 9.2.2.3.1
Move the negative in front of the fraction.
Step 10
The final solution is all the values that make true.
Step 11
Factor out of .
Tap for more steps...
Step 11.1
Factor out of .
Step 11.2
Factor out of .
Step 11.3
Factor out of .
Step 11.4
Factor out of .
Step 11.5
Factor out of .
Step 12
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 13
Set equal to .
Step 14
Set equal to and solve for .
Tap for more steps...
Step 14.1
Set equal to .
Step 14.2
Solve for .
Tap for more steps...
Step 14.2.1
Use the quadratic formula to find the solutions.
Step 14.2.2
Substitute the values , , and into the quadratic formula and solve for .
Step 14.2.3
Simplify.
Tap for more steps...
Step 14.2.3.1
Simplify the numerator.
Tap for more steps...
Step 14.2.3.1.1
One to any power is one.
Step 14.2.3.1.2
Multiply .
Tap for more steps...
Step 14.2.3.1.2.1
Multiply by .
Step 14.2.3.1.2.2
Multiply by .
Step 14.2.3.1.3
Subtract from .
Step 14.2.3.1.4
Rewrite as .
Step 14.2.3.1.5
Rewrite as .
Step 14.2.3.1.6
Rewrite as .
Step 14.2.3.2
Multiply by .
Step 14.2.4
Simplify the expression to solve for the portion of the .
Tap for more steps...
Step 14.2.4.1
Simplify the numerator.
Tap for more steps...
Step 14.2.4.1.1
One to any power is one.
Step 14.2.4.1.2
Multiply .
Tap for more steps...
Step 14.2.4.1.2.1
Multiply by .
Step 14.2.4.1.2.2
Multiply by .
Step 14.2.4.1.3
Subtract from .
Step 14.2.4.1.4
Rewrite as .
Step 14.2.4.1.5
Rewrite as .
Step 14.2.4.1.6
Rewrite as .
Step 14.2.4.2
Multiply by .
Step 14.2.4.3
Change the to .
Step 14.2.4.4
Rewrite as .
Step 14.2.4.5
Factor out of .
Step 14.2.4.6
Factor out of .
Step 14.2.4.7
Move the negative in front of the fraction.
Step 14.2.5
Simplify the expression to solve for the portion of the .
Tap for more steps...
Step 14.2.5.1
Simplify the numerator.
Tap for more steps...
Step 14.2.5.1.1
One to any power is one.
Step 14.2.5.1.2
Multiply .
Tap for more steps...
Step 14.2.5.1.2.1
Multiply by .
Step 14.2.5.1.2.2
Multiply by .
Step 14.2.5.1.3
Subtract from .
Step 14.2.5.1.4
Rewrite as .
Step 14.2.5.1.5
Rewrite as .
Step 14.2.5.1.6
Rewrite as .
Step 14.2.5.2
Multiply by .
Step 14.2.5.3
Change the to .
Step 14.2.5.4
Rewrite as .
Step 14.2.5.5
Factor out of .
Step 14.2.5.6
Factor out of .
Step 14.2.5.7
Move the negative in front of the fraction.
Step 14.2.6
The final answer is the combination of both solutions.
Step 15
The final solution is all the values that make true.
Step 16
Since the roots of an equation are the points where the solution is , set each root as a factor of the equation that equals .
Step 17
Simplify.
Tap for more steps...
Step 17.1
Subtract from .
Step 17.2
Subtract from .
Step 17.3
Multiply .
Tap for more steps...
Step 17.3.1
Raise to the power of .
Step 17.3.2
Raise to the power of .
Step 17.3.3
Use the power rule to combine exponents.
Step 17.3.4
Add and .
Step 17.4
Subtract from .
Step 17.5
Subtract from .
Step 17.6
Subtract from .
Step 17.7
Multiply .
Tap for more steps...
Step 17.7.1
Raise to the power of .
Step 17.7.2
Raise to the power of .
Step 17.7.3
Use the power rule to combine exponents.
Step 17.7.4
Add and .