Question 7 of 10, Step 2 of 2
Consider the following quadratic equation:
Step 2 of
formula

Ask by Harrington Fernandez. in the United States

Mar 17,2025

Question

Question 7 of 10, Step 2 of 2 Consider the following quadratic equation: Step 2 of $$ 2:-4 x^{2}+2=x $$ formula $$ x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} $$

UpStudy AI · Accepted Answer

We start with the equation
$$
-4 x^2 + 2 = x.
$$
First, rearrange the equation so that all terms are on one side:
$$
-4 x^2 - x + 2 = 0.
$$

Here, we identify the coefficients:
$$
a = -4,\quad b = -1,\quad c = 2.
$$

Next, substitute these into the quadratic formula
$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
$$

Substitute $$ a = -4 $$, $$ b = -1 $$, and $$ c = 2 $$:
$$
x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(-4)(2)}}{2(-4)}.
$$

Simplify the numerator:
$$
-(-1) = 1.
$$

Calculate the discriminant:
$$
(-1)^2 - 4(-4)(2) = 1 + 32 = 33.
$$

Now, the formula becomes:
$$
x = \frac{1 \pm \sqrt{33}}{-8}.
$$

This can also be written by factoring out a $$-1$$ in the numerator:
$$
x = -\frac{1 \pm \sqrt{33}}{8}.
$$

Thus, the solutions are:
$$
x = -\frac{1 + \sqrt{33}}{8} \quad \text{or} \quad x = -\frac{1 - \sqrt{33}}{8}.
$$
The solutions are $$ x = -\frac{1 + \sqrt{33}}{8} $$ and $$ x = -\frac{1 - \sqrt{33}}{8} $$.

Question 7 of 10, Step 2 of 2
Consider the following quadratic equation:
Step 2 of
formula

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions

Question 7 of 10, Step 2 of 2 Consider the following quadratic equation: Step 2 of formula