Solve Equations by Substitutions

The powerful method of substitution is used to solve different types of equations.

Examples with Solutions

Example 1

Solve the equation
x - 3 √ x = - 2

Solution to Example 1

Example 2

Solve the equation Use the method of substitution to solve the equation
1 / (x - 1) 2 - 1 / (x - 1) - 2 = 0

Solution to Example 2

Example 3

Solve the equation Use the method of substitution to solve the equation
- (x + 3) 6 + 4 (x + 3) 3 = - 21

Solution to Example 3

Example 4

Solve the equation Use the method of substitution to solve the equation
3 e 2 x - e x - 2 = 0

Solution to Example 4


Example 5

Solve the equation Use the method of substitution to solve the equation
sin 2 x - 4 sin x - 5 = 0
for x in the interval [ 0 , 2 π ). Give x in radians.

Solution to Example 5

More References and links

Solve Equations, Systems of Equations and Inequalities.