Question Find the value of $\frac{-b-\sqrt{b^{2}-4ac}}{2a}$ when $a=11, b=7$ , and $c=-4$ .

Studdy Solution

STEP 1

Assumptions
1. The equation is $\frac{-b-\sqrt{b^{2}-4 a c}}{2 a}$
2. The values of $a$ , $b$ and $c$ are given as $a=11$ , $b=7$ and $c=-4$ respectively

STEP 2

First, we need to substitute the given values of $a$ , $b$ and $c$ into the equation.
$\frac{-b-\sqrt{b^{2}-4 a c}}{2 a} = \frac{-7-\sqrt{7^{2}-4 \cdot 11 \cdot -4}}{2 \cdot 11}$

STEP 3

Calculate the value inside the square root.
$\sqrt{7^{2}-4 \cdot 11 \cdot -4} = \sqrt{49-(-176)}$

STEP 4

Simplify the value inside the square root.
$\sqrt{49-(-176)} = \sqrt{49+176} = \sqrt{225}$

STEP 5

Calculate the square root.
$\sqrt{225} = 15$

STEP 6

Substitute the value of the square root back into the equation.
$\frac{-7-15}{2 \cdot 11}$

STEP 7

Calculate the numerator.
$-7-15 = -22$

STEP 8

Substitute the value of the numerator back into the equation.
$\frac{-22}{2 \cdot 11}$

STEP 9

Calculate the denominator.
$2 \cdot 11 = 22$

STEP 10

Substitute the value of the denominator back into the equation.
$\frac{-22}{22}$

STEP 11

Calculate the value of the equation.
$\frac{-22}{22} = -1$
The value of $\frac{-b-\sqrt{b^{2}-4 a c}}{2 a}$ when $a=11$ , $b=7$ and $c=-4$ is $-1$ .

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