Solve (18-b)^2 - 2b - 17

Question

Simplify the expression

307 - 38 b + b^{2}

Show Solution

b_{1} = 19 - 36, b_{2} = 19 + 36

Alternative Form

b_{1} \approx 11.651531, b_{2} \approx 26.348469

Evaluate

(18 - b)^{2} - 2 b - 17

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

(18 - b)^{2} - 2 b - 17 = 0

Subtract the terms

More Steps

324 - 38 b + b^{2} - 17 = 0

Subtract the numbers

307 - 38 b + b^{2} = 0

Rewrite in standard form

b^{2} - 38 b + 307 = 0

Substitute a= 1,b= - 38 and c= 307 into the quadratic formula b = \frac{- b \pm b ^{2} - 4 a c}{2 a}

b = \frac{38 \pm ( - 38 ) ^{2} - 4 \times 307}{2}

Simplify the expression

More Steps

b = \frac{38 \pm 216}{2}

Simplify the radical expression

More Steps

b = \frac{38 \pm 6 6}{2}

Separate the equation into 2 possible cases

b = \frac{38 + 6 6}{2} b = \frac{38 - 6 6}{2}

Simplify the expression

More Steps

b = 19 + 36 b = \frac{38 - 6 6}{2}

Simplify the expression

More Steps

b = 19 + 36 b = 19 - 36

Solution

b_{1} = 19 - 36, b_{2} = 19 + 36

Alternative Form

b_{1} \approx 11.651531, b_{2} \approx 26.348469

Show Solution