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Solve the equation 2, x, squared, minus, x, minus, 29, equals, 152x
2
−x−29=15 to the nearest tenth.
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Attempt 2 out of 5

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Answer 1

To solve the equation \(2x^2 - x - 29 = 152\), we first need to set the equation to zero.

1. Move all terms to one side of the equation:
\[
2x^2 - x - 29 - 152 = 0
\]
Simplifying this gives:
\[
2x^2 - x - 181 = 0
\]

2. Now we can use the quadratic formula. The quadratic formula states:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
where \(a = 2\), \(b = -1\), and \(c = -181\).

3. First, calculate the discriminant:
\[
b^2 - 4ac = (-1)^2 - 4 \cdot 2 \cdot (-181)
\]
\[
= 1 + 1456
\]
\[
= 1457
\]

4. Now plug in the values into the quadratic formula:
\[
x = \frac{-(-1) \pm \sqrt{1457}}{2 \cdot 2}
\]
\[
x = \frac{1 \pm \sqrt{1457}}{4}
\]

5. Calculate \( \sqrt{1457} \):
\[
\sqrt{1457} \approx 38.16 \quad \text{(to two decimal places)}
\]

6. Now substitute back into the formula:
\[
x = \frac{1 \pm 38.16}{4}
\]

This will give us two possible solutions:
- For the plus sign:
\[
x \approx \frac{1 + 38.16}{4} \approx \frac{39.16}{4} \approx 9.79
\]
- For the minus sign:
\[
x \approx \frac{1 - 38.16}{4} \approx \frac{-37.16}{4} \approx -9.29
\]

7. Round the answers to the nearest tenth:
- The positive solution is \(x \approx 9.8\)
- The negative solution is \(x \approx -9.3\)

Therefore, the solutions to the equation \(2x^2 - x - 181 = 0\) are:
\[
x \approx 9.8 \quad \text{and} \quad x \approx -9.3
\]