Solve 4b^2+12b+36

Question

Factor the expression

4 (b^{2} + 3 b + 9)

Show Solution

b_{1} = - \frac{3}{2} - \frac{3 3}{2} i, b_{2} = - \frac{3}{2} + \frac{3 3}{2} i

Alternative Form

b_{1} \approx - 1.5 - 2.598076 i, b_{2} \approx - 1.5 + 2.598076 i

Evaluate

4 b^{2} + 12 b + 36

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

4 b^{2} + 12 b + 36 = 0

Substitute a= 4,b= 12 and c= 36 into the quadratic formula b = \frac{- b \pm b ^{2} - 4 a c}{2 a}

b = \frac{- 12 \pm 1 2 ^{2} - 4 \times 4 \times 36}{2 \times 4}

Simplify the expression

b = \frac{- 12 \pm 1 2 ^{2} - 4 \times 4 \times 36}{8}

Simplify the expression

More Steps

b = \frac{- 12 \pm - 432}{8}

Simplify the radical expression

More Steps

b = \frac{- 12 \pm 12 3 \times i}{8}

Separate the equation into 2 possible cases

b = \frac{- 12 + 12 3 \times i}{8} b = \frac{- 12 - 12 3 \times i}{8}

Simplify the expression

More Steps

b = - \frac{3}{2} + \frac{3 3}{2} i b = \frac{- 12 - 12 3 \times i}{8}

Simplify the expression

More Steps

b = - \frac{3}{2} + \frac{3 3}{2} i b = - \frac{3}{2} - \frac{3 3}{2} i

Solution

b_{1} = - \frac{3}{2} - \frac{3 3}{2} i, b_{2} = - \frac{3}{2} + \frac{3 3}{2} i

Alternative Form

b_{1} \approx - 1.5 - 2.598076 i, b_{2} \approx - 1.5 + 2.598076 i

Show Solution