Solve 3a^2 - 5 pi/2 pi^2/4

Question

Simplify the expression

3 a^{2} - \frac{5 π ^{3}}{8}

Show Solution

\frac{1}{8} (24 a^{2} - 5 π^{3})

Show Solution

a_{1} = - \frac{π 30 π}{12}, a_{2} = \frac{π 30 π}{12}

Alternative Form

a_{1} \approx - 2.541582, a_{2} \approx 2.541582

Evaluate

3 a^{2} - (5 \times \frac{π}{2}) \times \frac{π ^{2}}{4}

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

3 a^{2} - (5 \times \frac{π}{2}) \times \frac{π ^{2}}{4} = 0

Multiply the numbers

3 a^{2} - \frac{5 π}{2} \times \frac{π ^{2}}{4} = 0

Multiply the numbers

More Steps

3 a^{2} - \frac{5 π ^{3}}{8} = 0

Move the constant to the right-hand side and change its sign

3 a^{2} = 0 + \frac{5 π ^{3}}{8}

Add the terms

3 a^{2} = \frac{5 π ^{3}}{8}

Multiply by the reciprocal

3 a^{2} \times \frac{1}{3} = \frac{5 π ^{3}}{8} \times \frac{1}{3}

Multiply

a^{2} = \frac{5 π ^{3}}{8} \times \frac{1}{3}

Multiply

More Steps

a^{2} = \frac{5 π ^{3}}{24}

Take the root of both sides of the equation and remember to use both positive and negative roots

a = \pm \frac{5 π ^{3}}{24}

Simplify the expression

More Steps

a = \pm \frac{π 30 π}{12}

Separate the equation into 2 possible cases

a = \frac{π 30 π}{12} a = - \frac{π 30 π}{12}

Solution

a_{1} = - \frac{π 30 π}{12}, a_{2} = \frac{π 30 π}{12}

Alternative Form

a_{1} \approx - 2.541582, a_{2} \approx 2.541582

Show Solution