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Solve the following equation using the quadratic formula: 3x² + 16x + 5 = 0?

User Genadinik
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Answer:

To solve the equation 3x² + 16x + 5 = 0, we can use the quadratic formula. The quadratic formula is a formula that provides the solutions for any quadratic equation in the form ax² + bx + c = 0, where a, b, and c are constants.

The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x can be found using the following formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our given equation, we have a = 3, b = 16, and c = 5. Plugging these values into the quadratic formula, we get:

x = (-16 ± √(16² - 4 * 3 * 5)) / (2 * 3)

Simplifying further:

x = (-16 ± √(256 - 60)) / 6

x = (-16 ± √196) / 6

x = (-16 ± 14) / 6

This gives us two possible solutions for x:

1. x = (-16 + 14) / 6 = -2 / 6 = -1/3

2. x = (-16 - 14) / 6 = -30 / 6 = -5

Therefore, the solutions to the equation 3x² + 16x + 5 = 0 are x = -1/3 and x = -5.

User Jpnp
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