Solve the following equation. $$ 16 x^{2}+25=40 \mathrm{x} $$ Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The solution(s) is/are $$ x=\square $$ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no real solutions.

Question

UpStudy AI · Accepted Answer

We start with the equation:

$$
16x^2 + 25 = 40x
$$

**Step 1:** Rearrange the equation to set it equal to zero.

$$
16x^2 - 40x + 25 = 0
$$

**Step 2:** Identify the coefficients $$ a = 16 $$, $$ b = -40 $$, and $$ c = 25 $$.

**Step 3:** Compute the discriminant.

$$
\Delta = b^2 - 4ac = (-40)^2 - 4(16)(25) = 1600 - 1600 = 0
$$

**Step 4:** Since the discriminant is 0, there is one real solution (a repeated root). Use the formula:

$$
x = \frac{-b}{2a}
$$

Substitute the values of $$ b $$ and $$ a $$:

$$
x = \frac{-(-40)}{2(16)} = \frac{40}{32} = \frac{5}{4}
$$

Thus, the solution is:

$$
x = \frac{5}{4}
$$
The solution is $$ x = \frac{5}{4} $$.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions