How do you solve #x^2+15x=0#?

Question

HIX Tutor · Accepted Answer

undefined To solve $ x^2 + 15x = 0 $, follow these steps:

1. **Set the equation to zero**: It is already $ x^2 + 15x = 0 $.

2. **Factor the equation**: Look for common factors. 
   $$
   x(x + 15) = 0
   $$

3. **Set each factor to zero**:
   - $ x = 0 $
   - $ x + 15 = 0 $

4. **Solve for $ x $ in the second equation**:
   $$
   x + 15 = 0 \implies x = -15
   $$

5. **Write the answers**: 
   - $ x = 0 $
   - $ x = -15 $

So, the solutions are $ x = 0 $ and $ x = -15 $.

Eva Adamson · Answer

#color(blue)(x=0)# or #color(blue)(x=-15)# Factoring #x^2+15x=0# gives #color(white)("XX")x(x+15)=0# which implies either #color(white)("XX")x=0# or #color(white)("XX")(x+15=0)# #color(white)("XXXXX")rarr x=-15#

Genesis Allen · Answer

#x= 0, or x = -15#

The first approach is always to try and factorise the quadratic. Although this is not a trinomial, there is a common factor.

#x(x+15)=0#

Because the product is 0, one of the two factors must be equal to 0.

Either #x = 0, or x+ 15 =0," in which case " x = -15#

This gives two solutions, exactly what we expect with a quadratic.

Ethan Adkins · Answer

undefined To solve the quadratic equation $x^2 + 15x = 0$, we can factor out an $x$ from the left side:

$x(x + 15) = 0$

Now, we have a product of two factors equal to zero. According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. So, we set each factor to zero and solve for $x$:

$x = 0$ or $x + 15 = 0$

Solving $x + 15 = 0$ for $x$, we get:

$x = -15$

Therefore, the solutions to the equation $x^2 + 15x = 0$ are $x = 0$ and $x = -15$.