-8x^2+4x=-5 step by step to solve a quadratic formula

To solve the quadratic equation \(-8x^2 + 4x = -5\), we'll follow these steps using the quadratic formula. The quadratic formula is given by:

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

Where \(a\), \(b\), and \(c\) are the coefficients from the quadratic equation of the form \(ax^2 + bx + c = 0\).

### Step 1: Rewrite the equation in standard quadratic form
We need to move all terms to one side of the equation to set it equal to zero:

\[
-8x^2 + 4x + 5 = 0
\]

Now we have the equation in the form \(ax^2 + bx + c = 0\), where:
- \(a = -8\)
- \(b = 4\)
- \(c = 5\)

### Step 2: Identify the coefficients
We have:
- \(a = -8\)
- \(b = 4\)
- \(c = 5\)

### Step 3: Apply the quadratic formula
Substitute these values into the quadratic formula:

\[
x = \frac{-4 \pm \sqrt{4^2 - 4(-8)(5)}}{2(-8)}
\]

### Step 4: Simplify under the square root
First, calculate the discriminant (\(b^2 - 4ac\)):

\[
b^2 - 4ac = 4^2 - 4(-8)(5) = 16 + 160 = 176
\]

### Step 5: Simplify the square root
\[
\sqrt{176} = \sqrt{16 \times 11} = 4\sqrt{11}
\]

### Step 6: Complete the formula
Now substitute \(\sqrt{176} = 4\sqrt{11}\) into the formula:

\[
x = \frac{-4 \pm 4\sqrt{11}}{-16}
\]

### Step 7: Simplify the expression
Factor out the common factor of 4:

\[
x = \frac{4(-1 \pm \sqrt{11})}{-16} = \frac{-1 \pm \sqrt{11}}{4}
\]

### Step 8: Write the two solutions
So the two solutions for \(x\) are:

\[
x_1 = \frac{-1 + \sqrt{11}}{4}, \quad x_2 = \frac{-1 - \sqrt{11}}{4}
\]

Thus, the solutions are:

\[
x_1 = \frac{-1 + \sqrt{11}}{4}, \quad x_2 = \frac{-1 - \sqrt{11}}{4}
\]

---

Would you like more details or have any questions on this?

Here are 5 related questions for further exploration:

1. How do you determine if a quadratic equation has real or complex roots?
2. What happens when the discriminant is zero in a quadratic equation?
3. Can you solve a quadratic equation by completing the square instead of using the quadratic formula?
4. How do you factor a quadratic equation if it's factorable?
5. What are the properties of parabolas formed by quadratic equations?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) to understand the nature of the roots (real or complex).

-8x^2 + 4x = -5 step by step to solve a quadratic formula

Learn how to solve the quadratic equation -8x^2 + 4x + 5 = 0 using the quadratic formula, including a detailed step-by-step breakdown of the discriminant and simplification process. Suitable for students in Grades 9-10.

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