Solve 17a =a^32 - ScanMath

Question

Solve the equation

a_{1} = - \frac{34}{2}, a_{2} = 0, a_{3} = \frac{34}{2}

Alternative Form

a_{1} \approx - 2.915476, a_{2} = 0, a_{3} \approx 2.915476

Evaluate

17 a = a^{3} \times 2

Use the commutative property to reorder the terms

17 a = 2 a^{3}

Add or subtract both sides

17 a - 2 a^{3} = 0

Factor the expression

a (17 - 2 a^{2}) = 0

Separate the equation into 2 possible cases

a = 0 17 - 2 a^{2} = 0

Solve the equation

More Steps

Evaluate

17 - 2 a^{2} = 0

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

- 2 a^{2} = 0 - 17

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

- 2 a^{2} = - 17

Change the signs on both sides of the equation

2 a^{2} = 17

Divide both sides

\frac{2 a ^{2}}{2} = \frac{17}{2}

Divide the numbers

a^{2} = \frac{17}{2}

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

a = \pm \frac{17}{2}

Simplify the expression

More Steps

Evaluate

\frac{17}{2}

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

\frac{17}{2}

Multiply by the Conjugate

\frac{17 \times 2}{2 \times 2}

Multiply the numbers

\frac{34}{2 \times 2}

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

\frac{34}{2}

a = \pm \frac{34}{2}

Separate the equation into 2 possible cases

a = \frac{34}{2} a = - \frac{34}{2}

a = 0 a = \frac{34}{2} a = - \frac{34}{2}

Solution

a_{1} = - \frac{34}{2}, a_{2} = 0, a_{3} = \frac{34}{2}

Alternative Form

a_{1} \approx - 2.915476, a_{2} = 0, a_{3} \approx 2.915476

Show Solution