Sum of a number and it's square is 12.what is number

Let's solve the problem step by step.

Let the number be \( x \).

According to the problem, the sum of the number and its square is 12. So, we can write the equation as:

\[
x + x^2 = 12
\]

Now, rearrange the equation:

\[
x^2 + x - 12 = 0
\]

This is a quadratic equation. We can solve it using the quadratic formula:

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

For the equation \( x^2 + x - 12 = 0 \), the coefficients are:
- \( a = 1 \)
- \( b = 1 \)
- \( c = -12 \)

Substitute these values into the quadratic formula:

\[
x = \frac{-1 \pm \sqrt{1^2 - 4(1)(-12)}}{2(1)}
\]
\[
x = \frac{-1 \pm \sqrt{1 + 48}}{2}
\]
\[
x = \frac{-1 \pm \sqrt{49}}{2}
\]
\[
x = \frac{-1 \pm 7}{2}
\]

This gives us two possible solutions:

\[
x = \frac{-1 + 7}{2} = \frac{6}{2} = 3
\]
\[
x = \frac{-1 - 7}{2} = \frac{-8}{2} = -4
\]

So, the number can be either \( 3 \) or \( -4 \).

Would you like more details or have any questions?

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Here are five related questions:

1. How do you factor quadratic equations to solve them?
2. What is the significance of the discriminant in the quadratic formula?
3. Can quadratic equations have complex solutions?
4. How would you graph the quadratic equation \( x^2 + x - 12 = 0 \)?
5. What are the applications of quadratic equations in real life?

**Tip:** Always check your solutions by substituting them back into the original equation to verify they work correctly.

Learn how to solve the problem where the sum of a number and its square is 12. Detailed step-by-step solution using the quadratic formula. Suitable for Grades 7-9.

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