Solve n^3-7n 9 - ScanMath

Question

Simplify the expression

n^{3} - 63 n

Evaluate

n^{3} - 7 n \times 9

Solution

n^{3} - 63 n

Show Solution

n (n^{2} - 63)

Evaluate

n^{3} - 7 n \times 9

Multiply the terms

n^{3} - 63 n

Rewrite the expression

n \times n^{2} - n \times 63

Solution

n (n^{2} - 63)

Show Solution

n_{1} = - 37, n_{2} = 0, n_{3} = 37

Alternative Form

n_{1} \approx - 7.937254, n_{2} = 0, n_{3} \approx 7.937254

Evaluate

n^{3} - 7 n \times 9

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

n^{3} - 7 n \times 9 = 0

Multiply the terms

n^{3} - 63 n = 0

Factor the expression

n (n^{2} - 63) = 0

Separate the equation into 2 possible cases

n = 0 n^{2} - 63 = 0

Solve the equation

More Steps

Evaluate

n^{2} - 63 = 0

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

n^{2} = 0 + 63

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

n^{2} = 63

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

n = \pm 63

Simplify the expression

More Steps

Evaluate

63

Write the expression as a product where the root of one of the factors can be evaluated

9 \times 7

Write the number in exponential form with the base of 3

3^{2} \times 7

The root of a product is equal to the product of the roots of each factor

3^{2} \times 7

Reduce the index of the radical and exponent with 2

37

n = \pm 37

Separate the equation into 2 possible cases

n = 37 n = - 37

n = 0 n = 37 n = - 37

Solution

n_{1} = - 37, n_{2} = 0, n_{3} = 37

Alternative Form

n_{1} \approx - 7.937254, n_{2} = 0, n_{3} \approx 7.937254

Show Solution