Solve 4a^2 - 28a^45

Question

Simplify the expression

4 a^{2} - 140 a^{4}

Evaluate

4 a^{2} - 28 a^{4} \times 5

Solution

4 a^{2} - 140 a^{4}

Show Solution

4 a^{2} (1 - 35 a^{2})

Evaluate

4 a^{2} - 28 a^{4} \times 5

Multiply the terms

4 a^{2} - 140 a^{4}

Rewrite the expression

4 a^{2} - 4 a^{2} \times 35 a^{2}

Solution

4 a^{2} (1 - 35 a^{2})

Show Solution

a_{1} = - \frac{35}{35}, a_{2} = 0, a_{3} = \frac{35}{35}

Alternative Form

a_{1} \approx - 0.169031, a_{2} = 0, a_{3} \approx 0.169031

Evaluate

4 a^{2} - 28 a^{4} \times 5

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

4 a^{2} - 28 a^{4} \times 5 = 0

Multiply the terms

4 a^{2} - 140 a^{4} = 0

Factor the expression

4 a^{2} (1 - 35 a^{2}) = 0

Divide both sides

a^{2} (1 - 35 a^{2}) = 0

Separate the equation into 2 possible cases

a^{2} = 0 1 - 35 a^{2} = 0

The only way a power can be 0 is when the base equals 0

a = 0 1 - 35 a^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 35 a^{2} = 0

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

- 35 a^{2} = 0 - 1

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

- 35 a^{2} = - 1

Change the signs on both sides of the equation

35 a^{2} = 1

Divide both sides

\frac{35 a ^{2}}{35} = \frac{1}{35}

Divide the numbers

a^{2} = \frac{1}{35}

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

a = \pm \frac{1}{35}

Simplify the expression

More Steps

Evaluate

\frac{1}{35}

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

\frac{1}{35}

Simplify the radical expression

\frac{1}{35}

Multiply by the Conjugate

\frac{35}{35 \times 35}

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

\frac{35}{35}

a = \pm \frac{35}{35}

Separate the equation into 2 possible cases

a = \frac{35}{35} a = - \frac{35}{35}

a = 0 a = \frac{35}{35} a = - \frac{35}{35}

Solution

a_{1} = - \frac{35}{35}, a_{2} = 0, a_{3} = \frac{35}{35}

Alternative Form

a_{1} \approx - 0.169031, a_{2} = 0, a_{3} \approx 0.169031

Show Solution