Solve 60 = 12x 12 - 3x^24

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = 6 - 31, x_{2} = 6 + 31

Alternative Form

x_{1} \approx 0.432236, x_{2} \approx 11.567764

Evaluate

60 = 12 x \times 12 - 3 x^{2} \times 4

Simplify

More Steps

60 = 144 x - 12 x^{2}

Swap the sides

144 x - 12 x^{2} = 60

Move the expression to the left side

144 x - 12 x^{2} - 60 = 0

Rewrite in standard form

- 12 x^{2} + 144 x - 60 = 0

Multiply both sides

12 x^{2} - 144 x + 60 = 0

Substitute a= 12,b= - 144 and c= 60 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{144 \pm ( - 144 ) ^{2} - 4 \times 12 \times 60}{2 \times 12}

Simplify the expression

x = \frac{144 \pm ( - 144 ) ^{2} - 4 \times 12 \times 60}{24}

Simplify the expression

More Steps

x = \frac{144 \pm 17856}{24}

Simplify the radical expression

More Steps

x = \frac{144 \pm 24 31}{24}

Separate the equation into 2 possible cases

x = \frac{144 + 24 31}{24} x = \frac{144 - 24 31}{24}

Simplify the expression

More Steps

x = 6 + 31 x = \frac{144 - 24 31}{24}

Simplify the expression

More Steps

x = 6 + 31 x = 6 - 31

Solution

x_{1} = 6 - 31, x_{2} = 6 + 31

Alternative Form

x_{1} \approx 0.432236, x_{2} \approx 11.567764

Show Solution