Solve for $$ x $$ using the quadratic formula. $$ \begin{array}{c}x^{2}-16 x+15=0 \ x=[?], \ ext { Enter the smallest solution first. } \ ext { Quadratic Formula: } x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}\end{array} $$

Question

Solve for $$ x $$ using the quadratic formula. $$ \begin{array}{c}x^{2}-16 x+15=0 \ x=[?], \ 	ext { Enter the smallest solution first. } \ 	ext { Quadratic Formula: } x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}\end{array} $$

UpStudy AI · Accepted Answer

To solve the quadratic equation $$ x^2 - 16x + 15 = 0 $$ using the quadratic formula:

$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$

**Given:**
- $$ a = 1 $$
- $$ b = -16 $$
- $$ c = 15 $$

**Step 1: Calculate the Discriminant**
$$
\text{Discriminant} = b^2 - 4ac = (-16)^2 - 4(1)(15) = 256 - 60 = 196
$$

**Step 2: Compute the Square Root of the Discriminant**
$$
\sqrt{196} = 14
$$

**Step 3: Apply the Quadratic Formula**
$$
x = \frac{-(-16) \pm 14}{2 \times 1} = \frac{16 \pm 14}{2}
$$

**Step 4: Find the Two Solutions**
$$
x_1 = \frac{16 + 14}{2} = \frac{30}{2} = 15
$$
$$
x_2 = \frac{16 - 14}{2} = \frac{2}{2} = 1
$$

**Final Answer:**
$$
x = 1, \, 15
$$
The solutions are $$ x = 1 $$ and $$ x = 15 $$.

Solve for using the
quadratic formula.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions

Solve for using the quadratic formula.