Solve x^2-117x-387

Question

Find the roots

x_{1} = \frac{117 - 3 1693}{2}, x_{2} = \frac{117 + 3 1693}{2}

Alternative Form

x_{1} \approx - 3.219122, x_{2} \approx 120.219122

Evaluate

x^{2} - 117 x - 387

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

x^{2} - 117 x - 387 = 0

Substitute a= 1,b= - 117 and c= - 387 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{117 \pm ( - 117 ) ^{2} - 4 ( - 387 )}{2}

Simplify the expression

More Steps

Evaluate

(- 117)^{2} - 4 (- 387)

Multiply the numbers

More Steps

Evaluate

4 (- 387)

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

- 4 \times 387

Multiply the numbers

- 1548

(- 117)^{2} - (- 1548)

Rewrite the expression

11 7^{2} - (- 1548)

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

11 7^{2} + 1548

Evaluate the power

13689 + 1548

Add the numbers

15237

x = \frac{117 \pm 15237}{2}

Simplify the radical expression

More Steps

Evaluate

15237

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

9 \times 1693

Write the number in exponential form with the base of 3

3^{2} \times 1693

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

3^{2} \times 1693

Reduce the index of the radical and exponent with 2

31693

x = \frac{117 \pm 3 1693}{2}

Separate the equation into 2 possible cases

x = \frac{117 + 3 1693}{2} x = \frac{117 - 3 1693}{2}

Solution

x_{1} = \frac{117 - 3 1693}{2}, x_{2} = \frac{117 + 3 1693}{2}

Alternative Form

x_{1} \approx - 3.219122, x_{2} \approx 120.219122

Show Solution