Solve the following equation.
8 x squared plus 14 x equals 0
(1 point)
Responses
x equals Start Fraction 7 over 4 End Fraction or x = 0
Image with alt text: x equals Start Fraction 7 over 4 End Fraction or x = 0
x = 0
x = 0
x equals Start Fraction negative 7 over 4 End Fraction or x = 0
Image with alt text: x equals Start Fraction negative 7 over 4 End Fraction or x = 0
x equals Start Fraction negative 7 over 4 End Fraction
The correct answer is:
x equals Start Fraction negative 7 over 4 End Fraction or x = 0
To solve the equation 8x^2 + 14x = 0, we can factor out the common factor of 2x:
2x(4x + 7) = 0
Now we can set each factor equal to zero and solve for x:
2x = 0 or 4x + 7 = 0
For the first equation, dividing both sides by 2 gives us:
x = 0
For the second equation, subtracting 7 from both sides gives us:
4x = -7
Dividing both sides by 4 gives us:
x = -7/4
Therefore, the solutions of the equation are x = 0 and x = -7/4.