Solve -4(a^2)=-(5a^4)

Question

Solve the equation

a_{1} = - \frac{2 5}{5}, a_{2} = 0, a_{3} = \frac{2 5}{5}

Alternative Form

a_{1} \approx - 0.894427, a_{2} = 0, a_{3} \approx 0.894427

Evaluate

- 4 a^{2} = - 5 a^{4}

Add or subtract both sides

- 4 a^{2} - (- 5 a^{4}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 4 a^{2} + 5 a^{4} = 0

Factor the expression

a^{2} (- 4 + 5 a^{2}) = 0

Separate the equation into 2 possible cases

a^{2} = 0 - 4 + 5 a^{2} = 0

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

a = 0 - 4 + 5 a^{2} = 0

Solve the equation

More Steps

Evaluate

- 4 + 5 a^{2} = 0

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

5 a^{2} = 0 + 4

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

5 a^{2} = 4

Divide both sides

\frac{5 a ^{2}}{5} = \frac{4}{5}

Divide the numbers

a^{2} = \frac{4}{5}

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

a = \pm \frac{4}{5}

Simplify the expression

More Steps

Evaluate

\frac{4}{5}

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

\frac{4}{5}

Simplify the radical expression

\frac{2}{5}

Multiply by the Conjugate

\frac{2 5}{5 \times 5}

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

\frac{2 5}{5}

a = \pm \frac{2 5}{5}

Separate the equation into 2 possible cases

a = \frac{2 5}{5} a = - \frac{2 5}{5}

a = 0 a = \frac{2 5}{5} a = - \frac{2 5}{5}

Solution

a_{1} = - \frac{2 5}{5}, a_{2} = 0, a_{3} = \frac{2 5}{5}

Alternative Form

a_{1} \approx - 0.894427, a_{2} = 0, a_{3} \approx 0.894427

Show Solution

Solve the equation

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