Solve (7b^2-26b-53)/(b-5)

Question

Find the excluded values

b = 5

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7 b + 9 + \frac{- 8}{b - 5}

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b_{1} = \frac{13 - 6 15}{7}, b_{2} = \frac{13 + 6 15}{7}

Alternative Form

b_{1} \approx - 1.462557, b_{2} \approx 5.176843

Evaluate

\frac{7 b ^{2} - 26 b - 53}{b - 5}

To find the roots of the expression,set the expression equal to 0

\frac{7 b ^{2} - 26 b - 53}{b - 5} = 0

Find the domain

More Steps

\frac{7 b ^{2} - 26 b - 53}{b - 5} = 0, b \neq = 5

Calculate

\frac{7 b ^{2} - 26 b - 53}{b - 5} = 0

Cross multiply

7 b^{2} - 26 b - 53 = (b - 5) \times 0

Simplify the equation

7 b^{2} - 26 b - 53 = 0

Substitute a= 7,b= - 26 and c= - 53 into the quadratic formula b = \frac{- b \pm b ^{2} - 4 a c}{2 a}

b = \frac{26 \pm ( - 26 ) ^{2} - 4 \times 7 ( - 53 )}{2 \times 7}

Simplify the expression

b = \frac{26 \pm ( - 26 ) ^{2} - 4 \times 7 ( - 53 )}{14}

Simplify the expression

More Steps

b = \frac{26 \pm 2160}{14}

Simplify the radical expression

More Steps

b = \frac{26 \pm 12 15}{14}

Separate the equation into 2 possible cases

b = \frac{26 + 12 15}{14} b = \frac{26 - 12 15}{14}

Simplify the expression

More Steps

b = \frac{13 + 6 15}{7} b = \frac{26 - 12 15}{14}

Simplify the expression

More Steps

b = \frac{13 + 6 15}{7} b = \frac{13 - 6 15}{7}

Check if the solution is in the defined range

b = \frac{13 + 6 15}{7} b = \frac{13 - 6 15}{7}, b \neq = 5

Find the intersection of the solution and the defined range

b = \frac{13 + 6 15}{7} b = \frac{13 - 6 15}{7}

Solution

b_{1} = \frac{13 - 6 15}{7}, b_{2} = \frac{13 + 6 15}{7}

Alternative Form

b_{1} \approx - 1.462557, b_{2} \approx 5.176843

Show Solution