Solve 10n^2 - 35 = 65n

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - \frac{1}{2}, n_{2} = 7

Alternative Form

n_{1} = - 0.5, n_{2} = 7

Evaluate

10 n^{2} - 35 = 65 n

Move the expression to the left side

10 n^{2} - 35 - 65 n = 0

Factor the expression

More Steps

Evaluate

10 n^{2} - 35 - 65 n

Evaluate

10 n^{2} - 65 n - 35

Rewrite the expression

5 \times 2 n^{2} - 5 \times 13 n - 5 \times 7

Factor out 5 from the expression

5 (2 n^{2} - 13 n - 7)

Factor the expression

More Steps

Evaluate

2 n^{2} - 13 n - 7

Rewrite the expression

2 n^{2} + (1 - 14) n - 7

Calculate

2 n^{2} + n - 14 n - 7

Rewrite the expression

n \times 2 n + n - 7 \times 2 n - 7

Factor out n from the expression

n (2 n + 1) - 7 \times 2 n - 7

Factor out - 7 from the expression

n (2 n + 1) - 7 (2 n + 1)

Factor out 2 n + 1 from the expression

(n - 7) (2 n + 1)

5 (n - 7) (2 n + 1)

5 (n - 7) (2 n + 1) = 0

Divide the terms

(n - 7) (2 n + 1) = 0

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

n - 7 = 0 2 n + 1 = 0

Solve the equation for n

More Steps

Evaluate

n - 7 = 0

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

n = 0 + 7

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

n = 7

n = 7 2 n + 1 = 0

Solve the equation for n

More Steps

Evaluate

2 n + 1 = 0

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

2 n = 0 - 1

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

2 n = - 1

Divide both sides

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

Divide the numbers

n = \frac{- 1}{2}

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

n = - \frac{1}{2}

n = 7 n = - \frac{1}{2}

Solution

n_{1} = - \frac{1}{2}, n_{2} = 7

Alternative Form

n_{1} = - 0.5, n_{2} = 7

Show Solution