1. 2x + 8x = 0
2. 20x² - 4x = 0
3. 7x² + 18x = 10x² + 12x
Answer (1)
Let's solve the equations one by one.
Equation : 2 x + 8 x = 0
Combine like terms (which are terms with x in them): ( 2 + 8 ) x = 0 Simplify the expression: 10 x = 0
To solve for x , divide both sides by 10: x = 10 0 x = 0
So, the solution to the first equation is x = 0 .
Equation : 20 x 2 − 4 x = 0
Factor out the greatest common factor, which is 4 x : 4 x ( 5 x − 1 ) = 0
This gives us a product of two terms equal to zero. Using the Zero Product Property, set each term equal to zero:
4 x = 0
5 x − 1 = 0
Solve each equation:
4 x = 0 x = 0
5 x − 1 = 0 Add 1 to both sides: 5 x = 1 Divide by 5: x = 5 1
So, the solutions to the second equation are x = 0 and x = 5 1 .
Equation : 7 x 2 + 18 x = 10 x 2 + 12 x
First, move all terms to one side of the equation to set it to zero. Subtract 10 x 2 + 12 x from both sides: 7 x 2 + 18 x − 10 x 2 − 12 x = 0
Combine like terms: ( 7 x 2 − 10 x 2 ) + ( 18 x − 12 x ) = 0 − 3 x 2 + 6 x = 0
Factor out the greatest common factor, which is 3 x : 3 x ( − x + 2 ) = 0
Again, using the Zero Product Property, set each factor equal to zero:
3 x = 0
− x + 2 = 0
Solve each equation:
3 x = 0 x = 0
− x + 2 = 0 Subtract 2 from both sides: − x = − 2 Multiply by -1: x = 2
So, the solutions to the third equation are x = 0 and x = 2 .
