Solve the quadratic equation 46x² - 138x = 0 by factoring out the GCF.
• The solutions are x = -46 and x = 3.
• The solutions are x = 0 and x = 46.
• The solutions are x = 0 and x = 3.
The correct answer is:
• The solutions are x = 0 and x = 3.
To solve the quadratic equation by factoring out the greatest common factor (GCF), we can first factor out x from both terms:
46x² - 138x = 0
x(46x - 138) = 0
Now we can set each factor equal to zero and solve for x:
x = 0
46x - 138 = 0
For the second equation, we can add 138 to both sides and then divide by 46 to isolate x:
46x - 138 + 138 = 0 + 138
46x = 138
46x/46 = 138/46
x = 3
So the solutions to the quadratic equation 46x² - 138x = 0 are x = 0 and x = 3.