Solve 8-3 (x^2)= 72 (x-3)

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = - \frac{36 + 4 123}{3}, x_{2} = \frac{- 36 + 4 123}{3}

Alternative Form

x_{1} \approx - 26.787382, x_{2} \approx 2.787382

Evaluate

8 - 3 x^{2} = 72 (x - 3)

Expand the expression

More Steps

8 - 3 x^{2} = 72 x - 216

Move the expression to the left side

224 - 3 x^{2} - 72 x = 0

Rewrite in standard form

- 3 x^{2} - 72 x + 224 = 0

Multiply both sides

3 x^{2} + 72 x - 224 = 0

Substitute a= 3,b= 72 and c= - 224 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 72 \pm 7 2 ^{2} - 4 \times 3 ( - 224 )}{2 \times 3}

Simplify the expression

x = \frac{- 72 \pm 7 2 ^{2} - 4 \times 3 ( - 224 )}{6}

Simplify the expression

More Steps

x = \frac{- 72 \pm 7872}{6}

Simplify the radical expression

More Steps

x = \frac{- 72 \pm 8 123}{6}

Separate the equation into 2 possible cases

x = \frac{- 72 + 8 123}{6} x = \frac{- 72 - 8 123}{6}

Simplify the expression

More Steps

x = \frac{- 36 + 4 123}{3} x = \frac{- 72 - 8 123}{6}

Simplify the expression

More Steps

x = \frac{- 36 + 4 123}{3} x = - \frac{36 + 4 123}{3}

Solution

x_{1} = - \frac{36 + 4 123}{3}, x_{2} = \frac{- 36 + 4 123}{3}

Alternative Form

x_{1} \approx - 26.787382, x_{2} \approx 2.787382

Show Solution