twice the square of a positive number increased by three times the number is 14. find the number
answer choice:
a.) 4
b.) 5
c.) 7
d.) 2
Thanks :)
It's 2 M :)))))))))))
12 increased by three times a number
To solve this problem, let's represent the positive number as "x".
According to the given information, the equation would be: 2x^2 + 3x = 14.
To find the value of x, we need to solve this quadratic equation.
Step 1: Rearrange the equation in standard quadratic form, with one side equal to zero:
2x^2 + 3x - 14 = 0.
Step 2: Factor the quadratic equation if possible. However, in this case, it cannot be easily factored.
Step 3: We can use the quadratic formula to solve for x. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a).
For our equation, a = 2, b = 3, and c = -14.
Plugging in these values into the quadratic formula, we get:
x = (-3 ± √(3^2 - 4*2*(-14))) / (2*2).
Simplifying further:
x = (-3 ± √(9 + 112)) / 4.
x = (-3 ± √121) / 4.
x = (-3 ± 11) / 4.
Now we have two possible solutions:
x1 = (-3 + 11) / 4 = 8 / 4 = 2.
x2 = (-3 - 11) / 4 = -14 / 4 = -3.5.
Since the problem specifies a positive number, the solution is x = 2.
Let the positive square number be x
2x^2 + 3x = 14
solve for x:
2x^2 + 3x - 14 = 0
hint: it factors, remember to reject the negative answer.