Solve 1580 = n/2(8n-2)

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - \frac{79}{4}, n_{2} = 20

Alternative Form

n_{1} = - 19.75, n_{2} = 20

Evaluate

1580 = \frac{n}{2} (8 n - 2)

Multiply the terms

More Steps

Multiply the terms

\frac{n}{2} (8 n - 2)

Rewrite the expression

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

Cancel out the common factor 2

n (4 n - 1)

1580 = n (4 n - 1)

Swap the sides

n (4 n - 1) = 1580

Expand the expression

More Steps

Evaluate

n (4 n - 1)

Apply the distributive property

n \times 4 n - n \times 1

Multiply the terms

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Evaluate

n \times 4 n

Use the commutative property to reorder the terms

4 n \times n

Multiply the terms

4 n^{2}

4 n^{2} - n \times 1

Any expression multiplied by 1 remains the same

4 n^{2} - n

4 n^{2} - n = 1580

Move the expression to the left side

4 n^{2} - n - 1580 = 0

Factor the expression

More Steps

Evaluate

4 n^{2} - n - 1580

Rewrite the expression

4 n^{2} + (79 - 80) n - 1580

Calculate

4 n^{2} + 79 n - 80 n - 1580

Rewrite the expression

n \times 4 n + n \times 79 - 20 \times 4 n - 20 \times 79

Factor out n from the expression

n (4 n + 79) - 20 \times 4 n - 20 \times 79

Factor out - 20 from the expression

n (4 n + 79) - 20 (4 n + 79)

Factor out 4 n + 79 from the expression

(n - 20) (4 n + 79)

(n - 20) (4 n + 79) = 0

When the product of factors equals 0,at least one factor is 0

n - 20 = 0 4 n + 79 = 0

Solve the equation for n

More Steps

Evaluate

n - 20 = 0

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

n = 0 + 20

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

n = 20

n = 20 4 n + 79 = 0

Solve the equation for n

More Steps

Evaluate

4 n + 79 = 0

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

4 n = 0 - 79

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

4 n = - 79

Divide both sides

\frac{4 n}{4} = \frac{- 79}{4}

Divide the numbers

n = \frac{- 79}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

n = - \frac{79}{4}

n = 20 n = - \frac{79}{4}

Solution

n_{1} = - \frac{79}{4}, n_{2} = 20

Alternative Form

n_{1} = - 19.75, n_{2} = 20

Show Solution