Solve m^2-6m-2 ,<

Question

Find the roots

m_{1} = 3 - 11, m_{2} = 3 + 11

Alternative Form

m_{1} \approx - 0.316625, m_{2} \approx 6.316625

Evaluate

m^{2} - 6 m - 2

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

m^{2} - 6 m - 2 = 0

Substitute a= 1,b= - 6 and c= - 2 into the quadratic formula m = \frac{- b \pm b ^{2} - 4 a c}{2 a}

m = \frac{6 \pm ( - 6 ) ^{2} - 4 ( - 2 )}{2}

Simplify the expression

More Steps

Evaluate

(- 6)^{2} - 4 (- 2)

Multiply the numbers

More Steps

Evaluate

4 (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- 4 \times 2

Multiply the numbers

- 8

(- 6)^{2} - (- 8)

Rewrite the expression

6^{2} - (- 8)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

6^{2} + 8

Evaluate the power

36 + 8

Add the numbers

44

m = \frac{6 \pm 44}{2}

Simplify the radical expression

More Steps

Evaluate

44

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

4 \times 11

Write the number in exponential form with the base of 2

2^{2} \times 11

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

2^{2} \times 11

Reduce the index of the radical and exponent with 2

211

m = \frac{6 \pm 2 11}{2}

Separate the equation into 2 possible cases

m = \frac{6 + 2 11}{2} m = \frac{6 - 2 11}{2}

Simplify the expression

More Steps

Evaluate

m = \frac{6 + 2 11}{2}

Divide the terms

More Steps

Evaluate

\frac{6 + 2 11}{2}

Rewrite the expression

\frac{2 ( 3 + 11 )}{2}

Reduce the fraction

3 + 11

m = 3 + 11

m = 3 + 11 m = \frac{6 - 2 11}{2}

Simplify the expression

More Steps

Evaluate

m = \frac{6 - 2 11}{2}

Divide the terms

More Steps

Evaluate

\frac{6 - 2 11}{2}

Rewrite the expression

\frac{2 ( 3 - 11 )}{2}

Reduce the fraction

3 - 11

m = 3 - 11

m = 3 + 11 m = 3 - 11

Solution

m_{1} = 3 - 11, m_{2} = 3 + 11

Alternative Form

m_{1} \approx - 0.316625, m_{2} \approx 6.316625

Show Solution