solve x²+8x=48 by completing quadratic formula

To solve the quadratic equation \( x^2 + 8x = 48 \) using the quadratic formula, we first need to rewrite it in standard form \( ax^2 + bx + c = 0 \).

1. Rewrite the equation:
\[ x^2 + 8x - 48 = 0 \]

In this form:
- \( a = 1 \)
- \( b = 8 \)
- \( c = -48 \)

The quadratic formula is:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

2. Calculate the discriminant:
\[ b^2 - 4ac = 8^2 - 4(1)(-48) = 64 + 192 = 256 \]

3. Take the square root of the discriminant:
\[ \sqrt{256} = 16 \]

4. Substitute \( b \), the square root of the discriminant, and \( a \) into the formula:
\[ x = \frac{-8 \pm 16}{2(1)} \]

5. Simplify the expression for the two possible values of \( x \):
\[ x = \frac{-8 + 16}{2} = \frac{8}{2} = 4 \]
\[ x = \frac{-8 - 16}{2} = \frac{-24}{2} = -12 \]

Therefore, the solutions to the equation \( x^2 + 8x = 48 \) are:
\[ x = 4 \]
\[ x = -12 \]

Would you like details or have any questions about this solution?

Here are some related questions:

1. How can you verify the solutions to the equation \( x^2 + 8x = 48 \)?
2. What is the significance of the discriminant in the quadratic formula?
3. How do you factor the quadratic equation \( x^2 + 8x - 48 = 0 \)?
4. What is the vertex form of the equation \( x^2 + 8x - 48 = 0 \)?
5. How can you solve the equation \( x^2 + 8x = 48 \) by completing the square?

**Tip:** When solving quadratic equations, always ensure the equation is in the standard form \( ax^2 + bx + c = 0 \) before applying the quadratic formula.

Learn how to solve the quadratic equation x² + 8x = 48 step-by-step using the quadratic formula. This problem covers quadratic equations and their solutions, with detailed calculations and explanations. Suitable for students in Grades 9-12.

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