Solve (9a 7)-(2a^3)

Question

Simplify the expression

63 a - 2 a^{3}

Evaluate

(9 a \times 7) - 2 a^{3}

Solution

63 a - 2 a^{3}

Show Solution

a (63 - 2 a^{2})

Evaluate

(9 a \times 7) - 2 a^{3}

Multiply the terms

63 a - 2 a^{3}

Rewrite the expression

a \times 63 - a \times 2 a^{2}

Solution

a (63 - 2 a^{2})

Show Solution

a_{1} = - \frac{3 14}{2}, a_{2} = 0, a_{3} = \frac{3 14}{2}

Alternative Form

a_{1} \approx - 5.612486, a_{2} = 0, a_{3} \approx 5.612486

Evaluate

(9 a \times 7) - (2 a^{3})

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

(9 a \times 7) - (2 a^{3}) = 0

Multiply the terms

63 a - (2 a^{3}) = 0

Multiply the terms

63 a - 2 a^{3} = 0

Factor the expression

a (63 - 2 a^{2}) = 0

Separate the equation into 2 possible cases

a = 0 63 - 2 a^{2} = 0

Solve the equation

More Steps

Evaluate

63 - 2 a^{2} = 0

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

- 2 a^{2} = 0 - 63

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

- 2 a^{2} = - 63

Change the signs on both sides of the equation

2 a^{2} = 63

Divide both sides

\frac{2 a ^{2}}{2} = \frac{63}{2}

Divide the numbers

a^{2} = \frac{63}{2}

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

a = \pm \frac{63}{2}

Simplify the expression

More Steps

Evaluate

\frac{63}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{63}{2}

Simplify the radical expression

\frac{3 7}{2}

Multiply by the Conjugate

\frac{3 7 \times 2}{2 \times 2}

Multiply the numbers

\frac{3 14}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{3 14}{2}

a = \pm \frac{3 14}{2}

Separate the equation into 2 possible cases

a = \frac{3 14}{2} a = - \frac{3 14}{2}

a = 0 a = \frac{3 14}{2} a = - \frac{3 14}{2}

Solution

a_{1} = - \frac{3 14}{2}, a_{2} = 0, a_{3} = \frac{3 14}{2}

Alternative Form

a_{1} \approx - 5.612486, a_{2} = 0, a_{3} \approx 5.612486

Show Solution