How do I Use the Quadratic Formula to Solve 3x^2 + 9x + 6 = 0?

Question

In this question, we use the quadratic formula to solve the expression 5x2 + 11x + 2 = 0. The quadratic formula is [-b +- sqrt(b² - 4ac)] / 2a.

Answer 1

Follow this secret recipe to reach the solution in the easiest possible manner!

You have to know that the coefficient of x^2 is always (a). The coefficient of x is always (b). The last value is always (c).

Given the equation: 3x^2+9x+6=0:

a=3

b=9

c=6

Substitute in the quadratic formula using these 3 values (a, b, and c). See how easy this was!! Don't forget to use the quadratic formula once using a (+) sign between the (-b) and the square root and another time using a (-) sign between the (-b) and the square root to get the 2 different solutions.

I'm always happy to help. I offer online tutoring sessions for just $20/hr!

Answer 2

The answer is simple, "replace & calculate"!

Do not overthink it.

Try with a pen & piece of paper first, use digital boards & devices later.

Read & write each step-down.

Go through the calculations & make sure they make sense.

Keep it simple :).

Step 1:

1. Write the quadratic equation..........................................ax2 + bx + c = 0 or ax^2 + bx + c = 0
2. Write the quadratic problem to solve.............................5x2 + 11x + 2 = 0 or 5x^2 + 11x + 2 = 0

Compare the right sides............................................ .And get a=5, b=11, c = 2.

Step 2:

Plugin the a, b, & c values into the Quad formula:

x = ( -b +- SQRT( b^2 - 4ac) ) / (2a)

x = ( -11 +- SQRT( 11^2 - 4(5)(2)) ) / (2(5))

x = ( -11 +- SQRT( 121 - 40 ) ) / 10

x = ( -11 +- SQRT( 81 ) ) / 10

x = ( -11 +- 9 ) / 10

Step 3: The two answers are

x = ( -11 + 9 ) / 10 = -2/10 = -0.2 AND

x = ( -11 - 9 ) / 10 = -20/10 = -2.0

Answer 3

Hi Asked

I see your question says “how do I use”; to that I’d recommend that you simply plug the coefficients and constant into the given calculation.

This being a question under Algebra are we to assume that the student is familiar with the Quadratic Equation and the Quadratic Formula and recognizes the following; the Quadratic Formula helps us solve any Quadratic Equation brought into or given in the Standard or General Format of ax²+ bx + c = 0?

Does the student recognize and understand what a, b, and c are and their positions within a Quadratic Equation so that the Quadratic Formula can easily be applied as a solution for x.

If so then, it is quite convenient that both Quadratics are already in the Standard/General Format.

I noticed that a, b, and c were generously labeled in the solutions given. I certainly agree that simplifying where possible makes the calculation process faster. That said, if the student does not understand that a and b are always coefficients and c is always a constant in the Standard Form of the Quadratic Equation, they might not place them correctly into the Quadratic Formula.

Answer 4

Using the quadratic formula and checking our answers afterwards, we see that x = -1 and -2.

Answer 5

See the videa.