Solve x^2 - 55x -225

Question

Find the roots

x_{1} = \frac{55 - 5 157}{2}, x_{2} = \frac{55 + 5 157}{2}

Alternative Form

x_{1} \approx - 3.82491, x_{2} \approx 58.82491

Evaluate

x^{2} - 55 x - 225

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

x^{2} - 55 x - 225 = 0

Substitute a= 1,b= - 55 and c= - 225 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{55 \pm ( - 55 ) ^{2} - 4 ( - 225 )}{2}

Simplify the expression

More Steps

Evaluate

(- 55)^{2} - 4 (- 225)

Multiply the numbers

More Steps

Evaluate

4 (- 225)

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

- 4 \times 225

Multiply the numbers

- 900

(- 55)^{2} - (- 900)

Rewrite the expression

5 5^{2} - (- 900)

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

5 5^{2} + 900

Evaluate the power

3025 + 900

Add the numbers

3925

x = \frac{55 \pm 3925}{2}

Simplify the radical expression

More Steps

Evaluate

3925

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

25 \times 157

Write the number in exponential form with the base of 5

5^{2} \times 157

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

5^{2} \times 157

Reduce the index of the radical and exponent with 2

5157

x = \frac{55 \pm 5 157}{2}

Separate the equation into 2 possible cases

x = \frac{55 + 5 157}{2} x = \frac{55 - 5 157}{2}

Solution

x_{1} = \frac{55 - 5 157}{2}, x_{2} = \frac{55 + 5 157}{2}

Alternative Form

x_{1} \approx - 3.82491, x_{2} \approx 58.82491

Show Solution