Question $b^{2}-35 b+300=0$

Studdy Solution

STEP 1

1. The equation $b^2 - 35b + 300 = 0$ is a quadratic equation in the variable $b$ .
2. The solutions to the quadratic equation can be found using the quadratic formula, factoring, or completing the square.
3. The quadratic formula is given by $b = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A}$ , where $A$ , $B$ , and $C$ are the coefficients of the terms $b^2$ , $b$ , and the constant term, respectively.

STEP 2

1. Identify the coefficients $A$ , $B$ , and $C$ in the quadratic equation.
2. Apply the quadratic formula to find the solutions for $b$ .
3. Simplify the solutions to obtain the final values for $b$ .

STEP 3

Identify the coefficients $A$ , $B$ , and $C$ in the quadratic equation $b^2 - 35b + 300 = 0$ .
Here, $A = 1$ , $B = -35$ , and $C = 300$ .

STEP 4

Apply the quadratic formula $b = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A}$ using the identified coefficients.
$b = \frac{-(-35) \pm \sqrt{(-35)^2 - 4 \cdot 1 \cdot 300}}{2 \cdot 1}$

STEP 5

Simplify the expression inside the square root.
$b = \frac{35 \pm \sqrt{1225 - 1200}}{2}$ $b = \frac{35 \pm \sqrt{25}}{2}$

STEP 6

Simplify the square root and then the entire expression.
$b = \frac{35 \pm 5}{2}$

STEP 7

Calculate the two possible solutions for $b$ .
$b_1 = \frac{35 + 5}{2} = \frac{40}{2} = 20$
$b_2 = \frac{35 - 5}{2} = \frac{30}{2} = 15$

STEP 8

The solutions to the quadratic equation $b^2 - 35b + 300 = 0$ are $b = 20$ and $b = 15$ .
Therefore, the values for $b$ are $b = 20$ and $b = 15$ .

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