Solve x^2-3x-9 - ScanMath

Question

Find the roots

x_{1} = \frac{3 - 3 5}{2}, x_{2} = \frac{3 + 3 5}{2}

Alternative Form

x_{1} \approx - 1.854102, x_{2} \approx 4.854102

Evaluate

x^{2} - 3 x - 9

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

x^{2} - 3 x - 9 = 0

Substitute a= 1,b= - 3 and c= - 9 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{3 \pm ( - 3 ) ^{2} - 4 ( - 9 )}{2}

Simplify the expression

More Steps

Evaluate

(- 3)^{2} - 4 (- 9)

Multiply the numbers

More Steps

Evaluate

4 (- 9)

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

- 4 \times 9

Multiply the numbers

- 36

(- 3)^{2} - (- 36)

Rewrite the expression

3^{2} - (- 36)

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

3^{2} + 36

Evaluate the power

9 + 36

Add the numbers

45

x = \frac{3 \pm 45}{2}

Simplify the radical expression

More Steps

Evaluate

45

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

9 \times 5

Write the number in exponential form with the base of 3

3^{2} \times 5

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

3^{2} \times 5

Reduce the index of the radical and exponent with 2

35

x = \frac{3 \pm 3 5}{2}

Separate the equation into 2 possible cases

x = \frac{3 + 3 5}{2} x = \frac{3 - 3 5}{2}

Solution

x_{1} = \frac{3 - 3 5}{2}, x_{2} = \frac{3 + 3 5}{2}

Alternative Form

x_{1} \approx - 1.854102, x_{2} \approx 4.854102

Show Solution