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Answer :
To solve the equation [tex]\(15x^2 + 13x = 0\)[/tex], we can use the quadratic formula. However, another straightforward approach is to factor the equation.
1. Factor the Equation:
The given equation is:
[tex]\[
15x^2 + 13x = 0
\][/tex]
We can factor out [tex]\(x\)[/tex] from both terms:
[tex]\[
x(15x + 13) = 0
\][/tex]
2. Apply the Zero Product Property:
According to the zero product property, if [tex]\(ab = 0\)[/tex], then either [tex]\(a = 0\)[/tex] or [tex]\(b = 0\)[/tex]. So, we set each factor equal to zero:
- [tex]\(x = 0\)[/tex]
- [tex]\(15x + 13 = 0\)[/tex]
3. Solve for [tex]\(x\)[/tex]:
- The first solution is straightforward: [tex]\(x = 0\)[/tex].
- For the second equation:
[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]
Thus, the solutions to the equation [tex]\(15x^2 + 13x = 0\)[/tex] are [tex]\(x = 0\)[/tex] and [tex]\(x = -\frac{13}{15}\)[/tex]. Therefore, the correct answer is option a: [tex]\(x = -\frac{13}{15}, 0\)[/tex].
1. Factor the Equation:
The given equation is:
[tex]\[
15x^2 + 13x = 0
\][/tex]
We can factor out [tex]\(x\)[/tex] from both terms:
[tex]\[
x(15x + 13) = 0
\][/tex]
2. Apply the Zero Product Property:
According to the zero product property, if [tex]\(ab = 0\)[/tex], then either [tex]\(a = 0\)[/tex] or [tex]\(b = 0\)[/tex]. So, we set each factor equal to zero:
- [tex]\(x = 0\)[/tex]
- [tex]\(15x + 13 = 0\)[/tex]
3. Solve for [tex]\(x\)[/tex]:
- The first solution is straightforward: [tex]\(x = 0\)[/tex].
- For the second equation:
[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]
Thus, the solutions to the equation [tex]\(15x^2 + 13x = 0\)[/tex] are [tex]\(x = 0\)[/tex] and [tex]\(x = -\frac{13}{15}\)[/tex]. Therefore, the correct answer is option a: [tex]\(x = -\frac{13}{15}, 0\)[/tex].
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