To solve the equation \( 8x^2 + 14x = 0 \), you can factor out the common term.
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Factor out \( x \) from the equation: \[ x(8x + 14) = 0 \]
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This gives us two factors: \[ x = 0 \quad \text{or} \quad 8x + 14 = 0 \]
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Now, solve for \( x \) in the second factor: \[ 8x + 14 = 0 \] \[ 8x = -14 \] \[ x = -\frac{14}{8} \] \[ x = -\frac{7}{4} \]
So, the solutions to the equation \( 8x^2 + 14x = 0 \) are: \[ x = 0 \quad \text{and} \quad x = -\frac{7}{4} \]