Solve a^31:150 = a1

Question

Solve the equation

a_{1} = - 56, a_{2} = 0, a_{3} = 56

Alternative Form

a_{1} \approx - 12.247449, a_{2} = 0, a_{3} \approx 12.247449

Evaluate

a^{3} \times 1 \div 150 = a \times 1

Simplify

More Steps

Evaluate

a^{3} \times 1 \div 150

Any expression multiplied by 1 remains the same

a^{3} \div 150

Rewrite the expression

\frac{a ^{3}}{150}

\frac{a ^{3}}{150} = a \times 1

Any expression multiplied by 1 remains the same

\frac{a ^{3}}{150} = a

Cross multiply

a^{3} = 150 a

Move the expression to the left side

a^{3} - 150 a = 0

Factor the expression

a (a^{2} - 150) = 0

Separate the equation into 2 possible cases

a = 0 a^{2} - 150 = 0

Solve the equation

More Steps

Evaluate

a^{2} - 150 = 0

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

a^{2} = 0 + 150

Removing 0 doesn't change the value,so remove it from the expression

a^{2} = 150

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

a = \pm 150

Simplify the expression

More Steps

Evaluate

150

Write the expression as a product where the root of one of the factors can be evaluated

25 \times 6

Write the number in exponential form with the base of 5

5^{2} \times 6

The root of a product is equal to the product of the roots of each factor

5^{2} \times 6

Reduce the index of the radical and exponent with 2

56

a = \pm 56

Separate the equation into 2 possible cases

a = 56 a = - 56

a = 0 a = 56 a = - 56

Solution

a_{1} = - 56, a_{2} = 0, a_{3} = 56

Alternative Form

a_{1} \approx - 12.247449, a_{2} = 0, a_{3} \approx 12.247449

Show Solution