Solve x^(2 )- 12x - 2304

Question

Find the roots

x_{1} = 6 - 665, x_{2} = 6 + 665

Alternative Form

x_{1} \approx - 42.373546, x_{2} \approx 54.373546

Evaluate

x^{2} - 12 x - 2304

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

x^{2} - 12 x - 2304 = 0

Substitute a= 1,b= - 12 and c= - 2304 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{12 \pm ( - 12 ) ^{2} - 4 ( - 2304 )}{2}

Simplify the expression

More Steps

Evaluate

(- 12)^{2} - 4 (- 2304)

Multiply the numbers

More Steps

Evaluate

4 (- 2304)

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

- 4 \times 2304

Multiply the numbers

- 9216

(- 12)^{2} - (- 9216)

Rewrite the expression

1 2^{2} - (- 9216)

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

1 2^{2} + 9216

Evaluate the power

144 + 9216

Add the numbers

9360

x = \frac{12 \pm 9360}{2}

Simplify the radical expression

More Steps

Evaluate

9360

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

144 \times 65

Write the number in exponential form with the base of 12

1 2^{2} \times 65

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

1 2^{2} \times 65

Reduce the index of the radical and exponent with 2

1265

x = \frac{12 \pm 12 65}{2}

Separate the equation into 2 possible cases

x = \frac{12 + 12 65}{2} x = \frac{12 - 12 65}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{12 + 12 65}{2}

Divide the terms

More Steps

Evaluate

\frac{12 + 12 65}{2}

Rewrite the expression

\frac{2 ( 6 + 6 65 )}{2}

Reduce the fraction

6 + 665

x = 6 + 665

x = 6 + 665 x = \frac{12 - 12 65}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{12 - 12 65}{2}

Divide the terms

More Steps

Evaluate

\frac{12 - 12 65}{2}

Rewrite the expression

\frac{2 ( 6 - 6 65 )}{2}

Reduce the fraction

6 - 665

x = 6 - 665

x = 6 + 665 x = 6 - 665

Solution

x_{1} = 6 - 665, x_{2} = 6 + 665

Alternative Form

x_{1} \approx - 42.373546, x_{2} \approx 54.373546

Show Solution