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]
### 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]
