Solve 7a^2 32=7-40a

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

a_{1} = - \frac{5 + 123}{56}, a_{2} = \frac{- 5 + 123}{56}

Alternative Form

a_{1} \approx - 0.287331, a_{2} \approx 0.10876

Evaluate

7 a^{2} \times 32 = 7 - 40 a

Multiply the terms

224 a^{2} = 7 - 40 a

Move the expression to the left side

224 a^{2} - 7 + 40 a = 0

Rewrite in standard form

224 a^{2} + 40 a - 7 = 0

Substitute a= 224,b= 40 and c= - 7 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{- 40 \pm 4 0 ^{2} - 4 \times 224 ( - 7 )}{2 \times 224}

Simplify the expression

a = \frac{- 40 \pm 4 0 ^{2} - 4 \times 224 ( - 7 )}{448}

Simplify the expression

More Steps

a = \frac{- 40 \pm 7872}{448}

Simplify the radical expression

More Steps

a = \frac{- 40 \pm 8 123}{448}

Separate the equation into 2 possible cases

a = \frac{- 40 + 8 123}{448} a = \frac{- 40 - 8 123}{448}

Simplify the expression

More Steps

a = \frac{- 5 + 123}{56} a = \frac{- 40 - 8 123}{448}

Simplify the expression

More Steps

a = \frac{- 5 + 123}{56} a = - \frac{5 + 123}{56}

Solution

a_{1} = - \frac{5 + 123}{56}, a_{2} = \frac{- 5 + 123}{56}

Alternative Form

a_{1} \approx - 0.287331, a_{2} \approx 0.10876

Show Solution