Solve ( - 3d-7)-( - 9d^2-5d 9)

Question

Simplify the expression

42 d - 7 + 9 d^{2}

Show Solution

d_{1} = - \frac{7 + 2 14}{3}, d_{2} = \frac{- 7 + 2 14}{3}

Alternative Form

d_{1} \approx - 4.827772, d_{2} \approx 0.161105

Evaluate

(- 3 d - 7) - (- 9 d^{2} - 5 d \times 9)

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

(- 3 d - 7) - (- 9 d^{2} - 5 d \times 9) = 0

Remove the parentheses

- 3 d - 7 - (- 9 d^{2} - 5 d \times 9) = 0

Multiply the terms

- 3 d - 7 - (- 9 d^{2} - 45 d) = 0

Subtract the terms

More Steps

42 d - 7 + 9 d^{2} = 0

Rewrite in standard form

9 d^{2} + 42 d - 7 = 0

Substitute a= 9,b= 42 and c= - 7 into the quadratic formula d = \frac{- b \pm b ^{2} - 4 a c}{2 a}

d = \frac{- 42 \pm 4 2 ^{2} - 4 \times 9 ( - 7 )}{2 \times 9}

Simplify the expression

d = \frac{- 42 \pm 4 2 ^{2} - 4 \times 9 ( - 7 )}{18}

Simplify the expression

More Steps

d = \frac{- 42 \pm 2016}{18}

Simplify the radical expression

More Steps

d = \frac{- 42 \pm 12 14}{18}

Separate the equation into 2 possible cases

d = \frac{- 42 + 12 14}{18} d = \frac{- 42 - 12 14}{18}

Simplify the expression

More Steps

d = \frac{- 7 + 2 14}{3} d = \frac{- 42 - 12 14}{18}

Simplify the expression

More Steps

d = \frac{- 7 + 2 14}{3} d = - \frac{7 + 2 14}{3}

Solution

d_{1} = - \frac{7 + 2 14}{3}, d_{2} = \frac{- 7 + 2 14}{3}

Alternative Form

d_{1} \approx - 4.827772, d_{2} \approx 0.161105

Show Solution