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Solve the equation using the quadratic formula:

[tex]15x^2 + 13x = 0[/tex]

Please select the best answer from the choices provided:

A. [tex]x = -\frac{13}{15}, 0[/tex]

B. [tex]x = 0[/tex]

C. [tex]x = \frac{13}{15}, 0[/tex]

D. [tex]x = \pm \frac{13}{15}[/tex]

Answer :

To solve the equation [tex]\(15x^2 + 13x = 0\)[/tex], we can start by factoring it instead of using the quadratic formula because it simplifies easily.

### Step 1: Set Up the Equation

We have the quadratic equation:

[tex]\[ 15x^2 + 13x = 0 \][/tex]

### Step 2: Factor the Common Term

Factor out the common term, which is [tex]\(x\)[/tex]:

[tex]\[ x(15x + 13) = 0 \][/tex]

### Step 3: Set Each Factor to Zero

Now, solve each factor for [tex]\(x\)[/tex]:

1. [tex]\(x = 0\)[/tex]

2. [tex]\(15x + 13 = 0\)[/tex]

### Step 4: Solve for [tex]\(x\)[/tex]

For the second equation ([tex]\(15x + 13 = 0\)[/tex]), solve for [tex]\(x\)[/tex]:

[tex]\[ 15x + 13 = 0 \][/tex]

Subtract 13 from both sides:

[tex]\[ 15x = -13 \][/tex]

Divide both sides by 15:

[tex]\[ x = -\frac{13}{15} \][/tex]

### Conclusion

The solutions to the equation [tex]\(15x^2 + 13x = 0\)[/tex] are [tex]\(x = 0\)[/tex] and [tex]\(x = -\frac{13}{15}\)[/tex].

Based on the options provided, the correct answer is:

A: [tex]\(x = -\frac{13}{15}, 0\)[/tex]

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