3x2 + x – 14 = 0
3x2 + x – 14 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 3, b = 1, and c = -14.
x = (-1 ± sqrt(1^2 - 4(3)(-14))) / 2(3)
x = (-1 ± sqrt(1 + 168)) / 6
x = (-1 ± sqrt(169)) / 6
x = (-1 ± 13) / 6
x = 2 or x = -7/3
Therefore, the solutions to the equation 3x^2 + x - 14 = 0 are x = 2 or x = -7/3.
To solve the quadratic equation 3x^2 + x - 14 = 0, we can either use factoring, the quadratic formula, or completing the square. In this case, factoring seems to be the most straightforward method.
We are looking for two binomials that when multiplied equal to 3x^2 + x - 14. To find these binomials, we need two numbers that multiply to the product of the leading coefficient and the constant term (3 * -14 = -42) and add up to the middle coefficient (1).
Factors of -42:
1, -42
-1, 42
2, -21
-2, 21
3, -14
-3, 14
6, -7
-6, 7
None of these pairs of factors sum up to 1, so factoring is not possible in this case. We'll use the quadratic formula instead:
The quadratic formula is x = (-b ± √(b²-4ac)) / 2a, where a = 3, b = 1, and c = -14.
x = (-(1) ± √((1)²-4(3)(-14))) / 2(3)
x = (-1 ± √(1+168)) / 6
x = (-1 ± √169) / 6
x = (-1 ± 13) / 6
There are two possible solutions:
x = (-1 + 13) / 6 = 12 / 6 = 2
x = (-1 - 13) / 6 = -14 / 6 = -7/3
The solutions for the equation 3x^2 + x - 14 = 0 are x = 2 and x = -7/3.
To solve the equation 3x^2 + x - 14 = 0, we can use the quadratic formula. The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions (or roots) can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In our case, a = 3, b = 1, and c = -14. Substituting these values into the quadratic formula, we get:
x = (-(1) ± √((1)^2 - 4(3)(-14))) / 2(3)
Simplifying further:
x = (-1 ± √(1 + 168)) / 6
x = (-1 ± √169) / 6
x = (-1 ± 13) / 6
This gives us two possible values for x:
x₁ = (-1 + 13) / 6 = 12 / 6 = 2
x₂ = (-1 - 13) / 6 = -14 / 6 = -7/3
Therefore, the solutions to the equation 3x^2 + x - 14 = 0 are x = 2 and x = -7/3.