Solve x^2-4x-15 - ScanMath

Question

Find the roots

x_{1} = 2 - 19, x_{2} = 2 + 19

Alternative Form

x_{1} \approx - 2.358899, x_{2} \approx 6.358899

Evaluate

x^{2} - 4 x - 15

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

x^{2} - 4 x - 15 = 0

Substitute a= 1,b= - 4 and c= - 15 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{4 \pm ( - 4 ) ^{2} - 4 ( - 15 )}{2}

Simplify the expression

More Steps

Evaluate

(- 4)^{2} - 4 (- 15)

Multiply the numbers

More Steps

Evaluate

4 (- 15)

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

- 4 \times 15

Multiply the numbers

- 60

(- 4)^{2} - (- 60)

Rewrite the expression

4^{2} - (- 60)

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

4^{2} + 60

Evaluate the power

16 + 60

Add the numbers

76

x = \frac{4 \pm 76}{2}

Simplify the radical expression

More Steps

Evaluate

76

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

4 \times 19

Write the number in exponential form with the base of 2

2^{2} \times 19

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

2^{2} \times 19

Reduce the index of the radical and exponent with 2

219

x = \frac{4 \pm 2 19}{2}

Separate the equation into 2 possible cases

x = \frac{4 + 2 19}{2} x = \frac{4 - 2 19}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{4 + 2 19}{2}

Divide the terms

More Steps

Evaluate

\frac{4 + 2 19}{2}

Rewrite the expression

\frac{2 ( 2 + 19 )}{2}

Reduce the fraction

2 + 19

x = 2 + 19

x = 2 + 19 x = \frac{4 - 2 19}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{4 - 2 19}{2}

Divide the terms

More Steps

Evaluate

\frac{4 - 2 19}{2}

Rewrite the expression

\frac{2 ( 2 - 19 )}{2}

Reduce the fraction

2 - 19

x = 2 - 19

x = 2 + 19 x = 2 - 19

Solution

x_{1} = 2 - 19, x_{2} = 2 + 19

Alternative Form

x_{1} \approx - 2.358899, x_{2} \approx 6.358899

Show Solution