Solve x^2 -2x- 480

Question

Find the roots

x_{1} = 1 - 481, x_{2} = 1 + 481

Alternative Form

x_{1} \approx - 20.931712, x_{2} \approx 22.931712

Evaluate

x^{2} - 2 x - 480

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

x^{2} - 2 x - 480 = 0

Substitute a= 1,b= - 2 and c= - 480 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 \pm ( - 2 ) ^{2} - 4 ( - 480 )}{2}

Simplify the expression

More Steps

Evaluate

(- 2)^{2} - 4 (- 480)

Multiply the numbers

More Steps

Evaluate

4 (- 480)

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

- 4 \times 480

Multiply the numbers

- 1920

(- 2)^{2} - (- 1920)

Rewrite the expression

2^{2} - (- 1920)

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

2^{2} + 1920

Evaluate the power

4 + 1920

Add the numbers

1924

x = \frac{2 \pm 1924}{2}

Simplify the radical expression

More Steps

Evaluate

1924

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

4 \times 481

Write the number in exponential form with the base of 2

2^{2} \times 481

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

2^{2} \times 481

Reduce the index of the radical and exponent with 2

2481

x = \frac{2 \pm 2 481}{2}

Separate the equation into 2 possible cases

x = \frac{2 + 2 481}{2} x = \frac{2 - 2 481}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{2 + 2 481}{2}

Divide the terms

More Steps

Evaluate

\frac{2 + 2 481}{2}

Rewrite the expression

\frac{2 ( 1 + 481 )}{2}

Reduce the fraction

1 + 481

x = 1 + 481

x = 1 + 481 x = \frac{2 - 2 481}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{2 - 2 481}{2}

Divide the terms

More Steps

Evaluate

\frac{2 - 2 481}{2}

Rewrite the expression

\frac{2 ( 1 - 481 )}{2}

Reduce the fraction

1 - 481

x = 1 - 481

x = 1 + 481 x = 1 - 481

Solution

x_{1} = 1 - 481, x_{2} = 1 + 481

Alternative Form

x_{1} \approx - 20.931712, x_{2} \approx 22.931712

Show Solution