Solve a^2-14a^44 - ScanMath

Question

Simplify the expression

a^{2} - 56 a^{4}

Evaluate

a^{2} - 14 a^{4} \times 4

Solution

a^{2} - 56 a^{4}

Show Solution

a^{2} (1 - 56 a^{2})

Evaluate

a^{2} - 14 a^{4} \times 4

Multiply the terms

a^{2} - 56 a^{4}

Rewrite the expression

a^{2} - a^{2} \times 56 a^{2}

Solution

a^{2} (1 - 56 a^{2})

Show Solution

a_{1} = - \frac{14}{28}, a_{2} = 0, a_{3} = \frac{14}{28}

Alternative Form

a_{1} \approx - 0.133631, a_{2} = 0, a_{3} \approx 0.133631

Evaluate

a^{2} - 14 a^{4} \times 4

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

a^{2} - 14 a^{4} \times 4 = 0

Multiply the terms

a^{2} - 56 a^{4} = 0

Factor the expression

a^{2} (1 - 56 a^{2}) = 0

Separate the equation into 2 possible cases

a^{2} = 0 1 - 56 a^{2} = 0

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

a = 0 1 - 56 a^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 56 a^{2} = 0

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

- 56 a^{2} = 0 - 1

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

- 56 a^{2} = - 1

Change the signs on both sides of the equation

56 a^{2} = 1

Divide both sides

\frac{56 a ^{2}}{56} = \frac{1}{56}

Divide the numbers

a^{2} = \frac{1}{56}

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

a = \pm \frac{1}{56}

Simplify the expression

More Steps

Evaluate

\frac{1}{56}

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

\frac{1}{56}

Simplify the radical expression

\frac{1}{56}

Simplify the radical expression

\frac{1}{2 14}

Multiply by the Conjugate

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

Multiply the numbers

\frac{14}{28}

a = \pm \frac{14}{28}

Separate the equation into 2 possible cases

a = \frac{14}{28} a = - \frac{14}{28}

a = 0 a = \frac{14}{28} a = - \frac{14}{28}

Solution

a_{1} = - \frac{14}{28}, a_{2} = 0, a_{3} = \frac{14}{28}

Alternative Form

a_{1} \approx - 0.133631, a_{2} = 0, a_{3} \approx 0.133631

Show Solution