Solve a^2-25a-100

Question

Find the roots

a_{1} = \frac{25 - 5 41}{2}, a_{2} = \frac{25 + 5 41}{2}

Alternative Form

a_{1} \approx - 3.507811, a_{2} \approx 28.507811

Evaluate

a^{2} - 25 a - 100

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

a^{2} - 25 a - 100 = 0

Substitute a= 1,b= - 25 and c= - 100 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{25 \pm ( - 25 ) ^{2} - 4 ( - 100 )}{2}

Simplify the expression

More Steps

Evaluate

(- 25)^{2} - 4 (- 100)

Multiply the numbers

More Steps

Evaluate

4 (- 100)

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

- 4 \times 100

Multiply the numbers

- 400

(- 25)^{2} - (- 400)

Rewrite the expression

2 5^{2} - (- 400)

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

2 5^{2} + 400

Evaluate the power

625 + 400

Add the numbers

1025

a = \frac{25 \pm 1025}{2}

Simplify the radical expression

More Steps

Evaluate

1025

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

25 \times 41

Write the number in exponential form with the base of 5

5^{2} \times 41

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

5^{2} \times 41

Reduce the index of the radical and exponent with 2

541

a = \frac{25 \pm 5 41}{2}

Separate the equation into 2 possible cases

a = \frac{25 + 5 41}{2} a = \frac{25 - 5 41}{2}

Solution

a_{1} = \frac{25 - 5 41}{2}, a_{2} = \frac{25 + 5 41}{2}

Alternative Form

a_{1} \approx - 3.507811, a_{2} \approx 28.507811

Show Solution