Solve (4(n 1)^(2)-1)

Question

Simplify the expression

4 n^{2} - 1

Evaluate

4 (n \times 1)^{2} - 1

Solution

4 n^{2} - 1

Show Solution

(2 n - 1) (2 n + 1)

Evaluate

4 (n \times 1)^{2} - 1

Any expression multiplied by 1 remains the same

4 n^{2} - 1

Solution

(2 n - 1) (2 n + 1)

Show Solution

n_{1} = - \frac{1}{2}, n_{2} = \frac{1}{2}

Alternative Form

n_{1} = - 0.5, n_{2} = 0.5

Evaluate

(4 (n \times 1)^{2} - 1)

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

4 (n \times 1)^{2} - 1 = 0

Any expression multiplied by 1 remains the same

4 n^{2} - 1 = 0

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

4 n^{2} = 0 + 1

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

4 n^{2} = 1

Divide both sides

\frac{4 n ^{2}}{4} = \frac{1}{4}

Divide the numbers

n^{2} = \frac{1}{4}

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

n = \pm \frac{1}{4}

Simplify the expression

More Steps

Evaluate

\frac{1}{4}

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

\frac{1}{4}

Simplify the radical expression

\frac{1}{4}

Simplify the radical expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{1}{2}

n = \pm \frac{1}{2}

Separate the equation into 2 possible cases

n = \frac{1}{2} n = - \frac{1}{2}

Solution

n_{1} = - \frac{1}{2}, n_{2} = \frac{1}{2}

Alternative Form

n_{1} = - 0.5, n_{2} = 0.5

Show Solution