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Solve the equation x, squared, minus, 5, x, minus, 44, equals, minus, 7, xx
2
−5x−44=−7x to the nearest tenth.
Answer
Attempt 1 out of 5

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Answer 1

To solve the equation \( x^2 - 5x - 44 = -7x \), we first rearrange it to standard form.

1. Move all terms to one side:

\[
x^2 - 5x - 44 + 7x = 0
\]

This simplifies to:

\[
x^2 + 2x - 44 = 0
\]

2. Now, we can use the quadratic formula to solve for \( x \). The quadratic formula is given by:

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

Here, \( a = 1 \), \( b = 2 \), and \( c = -44 \).

3. Calculate the discriminant (\( b^2 - 4ac \)):

\[
b^2 - 4ac = (2)^2 - 4(1)(-44) = 4 + 176 = 180
\]

4. Now plug the values into the quadratic formula:

\[
x = \frac{-2 \pm \sqrt{180}}{2}
\]

5. First, simplify \( \sqrt{180} \):

\[
\sqrt{180} = \sqrt{36 \cdot 5} = 6\sqrt{5}
\]

6. Now substituting back, we have:

\[
x = \frac{-2 \pm 6\sqrt{5}}{2}
\]

Simplifying gives us:

\[
x = -1 \pm 3\sqrt{5}
\]

7. This results in two potential solutions:

\[
x_1 = -1 + 3\sqrt{5} \quad \text{and} \quad x_2 = -1 - 3\sqrt{5}
\]

8. Next, we can calculate these values. Numerical approximation for \( \sqrt{5} \approx 2.236 \):

- For \( x_1 \):

\[
x_1 = -1 + 3(2.236) \approx -1 + 6.708 \approx 5.708
\]

Rounding to the nearest tenth, \( x_1 \approx 5.7 \).

- For \( x_2 \):

\[
x_2 = -1 - 3(2.236) \approx -1 - 6.708 \approx -7.708
\]

Rounding to the nearest tenth, \( x_2 \approx -7.7 \).

Thus, the approximate solutions to the nearest tenth are:

\[
x \approx 5.7 \quad \text{and} \quad x \approx -7.7
\]