Solve x^2-5x-32 - ScanMath

Question

Find the roots

x_{1} = \frac{5 - 3 17}{2}, x_{2} = \frac{5 + 3 17}{2}

Alternative Form

x_{1} \approx - 3.684658, x_{2} \approx 8.684658

Evaluate

x^{2} - 5 x - 32

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

x^{2} - 5 x - 32 = 0

Substitute a= 1,b= - 5 and c= - 32 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{5 \pm ( - 5 ) ^{2} - 4 ( - 32 )}{2}

Simplify the expression

More Steps

Evaluate

(- 5)^{2} - 4 (- 32)

Multiply the numbers

More Steps

Evaluate

4 (- 32)

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

- 4 \times 32

Multiply the numbers

- 128

(- 5)^{2} - (- 128)

Rewrite the expression

5^{2} - (- 128)

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^{2} + 128

Evaluate the power

25 + 128

Add the numbers

153

x = \frac{5 \pm 153}{2}

Simplify the radical expression

More Steps

Evaluate

153

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

9 \times 17

Write the number in exponential form with the base of 3

3^{2} \times 17

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

3^{2} \times 17

Reduce the index of the radical and exponent with 2

317

x = \frac{5 \pm 3 17}{2}

Separate the equation into 2 possible cases

x = \frac{5 + 3 17}{2} x = \frac{5 - 3 17}{2}

Solution

x_{1} = \frac{5 - 3 17}{2}, x_{2} = \frac{5 + 3 17}{2}

Alternative Form

x_{1} \approx - 3.684658, x_{2} \approx 8.684658

Show Solution