Solve x^(2)-36x-108

Question

Find the roots

x_{1} = 18 - 123, x_{2} = 18 + 123

Alternative Form

x_{1} \approx - 2.78461, x_{2} \approx 38.78461

Evaluate

x^{2} - 36 x - 108

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

x^{2} - 36 x - 108 = 0

Substitute a= 1,b= - 36 and c= - 108 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{36 \pm ( - 36 ) ^{2} - 4 ( - 108 )}{2}

Simplify the expression

More Steps

Evaluate

(- 36)^{2} - 4 (- 108)

Multiply the numbers

More Steps

Evaluate

4 (- 108)

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

- 4 \times 108

Multiply the numbers

- 432

(- 36)^{2} - (- 432)

Rewrite the expression

3 6^{2} - (- 432)

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

3 6^{2} + 432

Evaluate the power

1296 + 432

Add the numbers

1728

x = \frac{36 \pm 1728}{2}

Simplify the radical expression

More Steps

Evaluate

1728

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

576 \times 3

Write the number in exponential form with the base of 24

2 4^{2} \times 3

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

2 4^{2} \times 3

Reduce the index of the radical and exponent with 2

243

x = \frac{36 \pm 24 3}{2}

Separate the equation into 2 possible cases

x = \frac{36 + 24 3}{2} x = \frac{36 - 24 3}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{36 + 24 3}{2}

Divide the terms

More Steps

Evaluate

\frac{36 + 24 3}{2}

Rewrite the expression

\frac{2 ( 18 + 12 3 )}{2}

Reduce the fraction

18 + 123

x = 18 + 123

x = 18 + 123 x = \frac{36 - 24 3}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{36 - 24 3}{2}

Divide the terms

More Steps

Evaluate

\frac{36 - 24 3}{2}

Rewrite the expression

\frac{2 ( 18 - 12 3 )}{2}

Reduce the fraction

18 - 123

x = 18 - 123

x = 18 + 123 x = 18 - 123

Solution

x_{1} = 18 - 123, x_{2} = 18 + 123

Alternative Form

x_{1} \approx - 2.78461, x_{2} \approx 38.78461

Show Solution