Solve 7n^28n^2-7n^25

Question

Simplify the expression

56 n^{4} - 35 n^{2}

Evaluate

7 n^{2} \times 8 n^{2} - 7 n^{2} \times 5

Multiply

More Steps

Multiply the terms

7 n^{2} \times 8 n^{2}

Multiply the terms

56 n^{2} \times n^{2}

Multiply the terms with the same base by adding their exponents

56 n^{2 + 2}

Add the numbers

56 n^{4}

56 n^{4} - 7 n^{2} \times 5

Solution

56 n^{4} - 35 n^{2}

Show Solution

7 n^{2} (8 n^{2} - 5)

Evaluate

7 n^{2} \times 8 n^{2} - 7 n^{2} \times 5

Solution

7 n^{2} (8 n^{2} - 5)

Show Solution

n_{1} = - \frac{10}{4}, n_{2} = 0, n_{3} = \frac{10}{4}

Alternative Form

n_{1} \approx - 0.790569, n_{2} = 0, n_{3} \approx 0.790569

Evaluate

7 n^{2} \times 8 n^{2} - 7 n^{2} \times 5

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

7 n^{2} \times 8 n^{2} - 7 n^{2} \times 5 = 0

Multiply

More Steps

Multiply the terms

7 n^{2} \times 8 n^{2}

Multiply the terms

56 n^{2} \times n^{2}

Multiply the terms with the same base by adding their exponents

56 n^{2 + 2}

Add the numbers

56 n^{4}

56 n^{4} - 7 n^{2} \times 5 = 0

Multiply the terms

56 n^{4} - 35 n^{2} = 0

Factor the expression

7 n^{2} (8 n^{2} - 5) = 0

Divide both sides

n^{2} (8 n^{2} - 5) = 0

Separate the equation into 2 possible cases

n^{2} = 0 8 n^{2} - 5 = 0

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

n = 0 8 n^{2} - 5 = 0

Solve the equation

More Steps

Evaluate

8 n^{2} - 5 = 0

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

8 n^{2} = 0 + 5

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

8 n^{2} = 5

Divide both sides

\frac{8 n ^{2}}{8} = \frac{5}{8}

Divide the numbers

n^{2} = \frac{5}{8}

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

n = \pm \frac{5}{8}

Simplify the expression

More Steps

Evaluate

\frac{5}{8}

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

\frac{5}{8}

Simplify the radical expression

\frac{5}{2 2}

Multiply by the Conjugate

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

Multiply the numbers

\frac{10}{2 2 \times 2}

Multiply the numbers

\frac{10}{4}

n = \pm \frac{10}{4}

Separate the equation into 2 possible cases

n = \frac{10}{4} n = - \frac{10}{4}

n = 0 n = \frac{10}{4} n = - \frac{10}{4}

Solution

n_{1} = - \frac{10}{4}, n_{2} = 0, n_{3} = \frac{10}{4}

Alternative Form

n_{1} \approx - 0.790569, n_{2} = 0, n_{3} \approx 0.790569

Show Solution