Solve x^2-6x-14 - ScanMath

Question

Find the roots

x_{1} = 3 - 23, x_{2} = 3 + 23

Alternative Form

x_{1} \approx - 1.795832, x_{2} \approx 7.795832

Evaluate

x^{2} - 6 x - 14

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

x^{2} - 6 x - 14 = 0

Substitute a= 1,b= - 6 and c= - 14 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 ( - 14 )}{2}

Simplify the expression

More Steps

Evaluate

(- 6)^{2} - 4 (- 14)

Multiply the numbers

More Steps

Evaluate

4 (- 14)

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

- 4 \times 14

Multiply the numbers

- 56

(- 6)^{2} - (- 56)

Rewrite the expression

6^{2} - (- 56)

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

6^{2} + 56

Evaluate the power

36 + 56

Add the numbers

92

x = \frac{6 \pm 92}{2}

Simplify the radical expression

More Steps

Evaluate

92

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

4 \times 23

Write the number in exponential form with the base of 2

2^{2} \times 23

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

2^{2} \times 23

Reduce the index of the radical and exponent with 2

223

x = \frac{6 \pm 2 23}{2}

Separate the equation into 2 possible cases

x = \frac{6 + 2 23}{2} x = \frac{6 - 2 23}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{6 + 2 23}{2}

Divide the terms

More Steps

Evaluate

\frac{6 + 2 23}{2}

Rewrite the expression

\frac{2 ( 3 + 23 )}{2}

Reduce the fraction

3 + 23

x = 3 + 23

x = 3 + 23 x = \frac{6 - 2 23}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{6 - 2 23}{2}

Divide the terms

More Steps

Evaluate

\frac{6 - 2 23}{2}

Rewrite the expression

\frac{2 ( 3 - 23 )}{2}

Reduce the fraction

3 - 23

x = 3 - 23

x = 3 + 23 x = 3 - 23

Solution

x_{1} = 3 - 23, x_{2} = 3 + 23

Alternative Form

x_{1} \approx - 1.795832, x_{2} \approx 7.795832

Show Solution