Solve (2n^2-5n-6) + (-n^2-3n+11)

Question

Simplify the expression

n^{2} - 8 n + 5

Show Solution

n_{1} = 4 - 11, n_{2} = 4 + 11

Alternative Form

n_{1} \approx 0.683375, n_{2} \approx 7.316625

Evaluate

(2 n^{2} - 5 n - 6) + (- n^{2} - 3 n + 11)

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

(2 n^{2} - 5 n - 6) + (- n^{2} - 3 n + 11) = 0

Remove the parentheses

2 n^{2} - 5 n - 6 + (- n^{2} - 3 n + 11) = 0

Remove the parentheses

2 n^{2} - 5 n - 6 - n^{2} - 3 n + 11 = 0

Calculate the sum or difference

More Steps

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

Substitute a= 1,b= - 8 and c= 5 into the quadratic formula n = \frac{- b \pm b ^{2} - 4 a c}{2 a}

n = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 5}{2}

Simplify the expression

More Steps

n = \frac{8 \pm 44}{2}

Simplify the radical expression

More Steps

n = \frac{8 \pm 2 11}{2}

Separate the equation into 2 possible cases

n = \frac{8 + 2 11}{2} n = \frac{8 - 2 11}{2}

Simplify the expression

More Steps

n = 4 + 11 n = \frac{8 - 2 11}{2}

Simplify the expression

More Steps

n = 4 + 11 n = 4 - 11

Solution

n_{1} = 4 - 11, n_{2} = 4 + 11

Alternative Form

n_{1} \approx 0.683375, n_{2} \approx 7.316625

Show Solution