Solve n(n+1)+1=91

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - 10, n_{2} = 9

Evaluate

n (n + 1) + 1 = 91

Expand the expression

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Evaluate

n (n + 1)

Apply the distributive property

n \times n + n \times 1

Multiply the terms

n^{2} + n \times 1

Any expression multiplied by 1 remains the same

n^{2} + n

n^{2} + n + 1 = 91

Move the expression to the left side

n^{2} + n - 90 = 0

Factor the expression

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Evaluate

n^{2} + n - 90

Rewrite the expression

n^{2} + (10 - 9) n - 90

Calculate

n^{2} + 10 n - 9 n - 90

Rewrite the expression

n \times n + n \times 10 - 9 n - 9 \times 10

Factor out n from the expression

n (n + 10) - 9 n - 9 \times 10

Factor out - 9 from the expression

n (n + 10) - 9 (n + 10)

Factor out n + 10 from the expression

(n - 9) (n + 10)

(n - 9) (n + 10) = 0

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

n - 9 = 0 n + 10 = 0

Solve the equation for n

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Evaluate

n - 9 = 0

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

n = 0 + 9

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

n = 9

n = 9 n + 10 = 0

Solve the equation for n

More Steps

Evaluate

n + 10 = 0

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

n = 0 - 10

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

n = - 10

n = 9 n = - 10

Solution

n_{1} = - 10, n_{2} = 9

Show Solution