Solve using the quadratic formula. $\newline$ $9m^2 + 9m + 2 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $m =$ _ or $m =$ _

View step-by-step help

Home

Math Problems

Precalculus

Solve a quadratic equation using the quadratic formula

Full solution

Q. Solve using the quadratic formula.

\newline

9m^2 + 9m + 2 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

m =

_____ or

m =

_____

Quadratic Formula Explanation: The quadratic formula is given by $m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a$ , $b$ , and $c$ are the coefficients of the terms in the quadratic equation $ax^2 + bx + c = 0$ . In this case, $a = 9$ , $b = 9$ , and $c = 2$ .
Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: $b^2 - 4ac$ . Here, it is $9^2 - 4(9)(2)$ .
Discriminant Calculation: Perform the calculation: $81 - 72 = 9$ .
Plug into Quadratic Formula: Now, plug the discriminant back into the quadratic formula to find the two possible values for $m$ . We have $m = \frac{-9 \pm \sqrt{9}}{2 \times 9}$ .
Simplify Square Root: Simplify the square root of the discriminant: $\sqrt{9} = 3$ .
Positive Square Root Calculation: Now, solve for the two possible values of $m$ . First, the positive square root: $m = (-9 + 3) / 18$ .
Positive Square Root Simplification: Perform the calculation: $m = \frac{-6}{18}$ .
Negative Square Root Calculation: Simplify the fraction: $m = -\frac{1}{3}$ .
Negative Square Root Simplification: Next, solve for $m$ using the negative square root: $m = ( -9 - 3 ) / 18$ .
Negative Square Root Simplification: Next, solve for $m$ using the negative square root: $m = (-9 - 3) / 18$ .Perform the calculation: $m = (-12) / 18$ .
Negative Square Root Simplification: Next, solve for $m$ using the negative square root: $m = (-9 - 3) / 18$ .Perform the calculation: $m = (-12) / 18$ .Simplify the fraction: $m = -2/3$ .