Solve x^(2)-2x-52

Question

Find the roots

x_{1} = 1 - 53, x_{2} = 1 + 53

Alternative Form

x_{1} \approx - 6.28011, x_{2} \approx 8.28011

Evaluate

x^{2} - 2 x - 52

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

x^{2} - 2 x - 52 = 0

Substitute a= 1,b= - 2 and c= - 52 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 \pm ( - 2 ) ^{2} - 4 ( - 52 )}{2}

Simplify the expression

More Steps

Evaluate

(- 2)^{2} - 4 (- 52)

Multiply the numbers

More Steps

Evaluate

4 (- 52)

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

- 4 \times 52

Multiply the numbers

- 208

(- 2)^{2} - (- 208)

Rewrite the expression

2^{2} - (- 208)

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} + 208

Evaluate the power

4 + 208

Add the numbers

212

x = \frac{2 \pm 212}{2}

Simplify the radical expression

More Steps

Evaluate

212

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

4 \times 53

Write the number in exponential form with the base of 2

2^{2} \times 53

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

2^{2} \times 53

Reduce the index of the radical and exponent with 2

253

x = \frac{2 \pm 2 53}{2}

Separate the equation into 2 possible cases

x = \frac{2 + 2 53}{2} x = \frac{2 - 2 53}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{2 + 2 53}{2}

Divide the terms

More Steps

Evaluate

\frac{2 + 2 53}{2}

Rewrite the expression

\frac{2 ( 1 + 53 )}{2}

Reduce the fraction

1 + 53

x = 1 + 53

x = 1 + 53 x = \frac{2 - 2 53}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{2 - 2 53}{2}

Divide the terms

More Steps

Evaluate

\frac{2 - 2 53}{2}

Rewrite the expression

\frac{2 ( 1 - 53 )}{2}

Reduce the fraction

1 - 53

x = 1 - 53

x = 1 + 53 x = 1 - 53

Solution

x_{1} = 1 - 53, x_{2} = 1 + 53

Alternative Form

x_{1} \approx - 6.28011, x_{2} \approx 8.28011

Show Solution