Solve h^220-41611

Question

Simplify the expression

20 h^{2} - 41611

Evaluate

h^{2} \times 20 - 41611

Solution

20 h^{2} - 41611

Show Solution

h_{1} = - \frac{208055}{10}, h_{2} = \frac{208055}{10}

Alternative Form

h_{1} \approx - 45.613046, h_{2} \approx 45.613046

Evaluate

h^{2} \times 20 - 41611

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

h^{2} \times 20 - 41611 = 0

Use the commutative property to reorder the terms

20 h^{2} - 41611 = 0

Move the constant to the right-hand side and change its sign

20 h^{2} = 0 + 41611

Removing 0 doesn't change the value,so remove it from the expression

20 h^{2} = 41611

Divide both sides

\frac{20 h ^{2}}{20} = \frac{41611}{20}

Divide the numbers

h^{2} = \frac{41611}{20}

Take the root of both sides of the equation and remember to use both positive and negative roots

h = \pm \frac{41611}{20}

Simplify the expression

More Steps

Evaluate

\frac{41611}{20}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{41611}{20}

Simplify the radical expression

More Steps

Evaluate

20

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

4 \times 5

Write the number in exponential form with the base of 2

2^{2} \times 5

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

2^{2} \times 5

Reduce the index of the radical and exponent with 2

25

\frac{41611}{2 5}

Multiply by the Conjugate

\frac{41611 \times 5}{2 5 \times 5}

Multiply the numbers

More Steps

Evaluate

41611 \times 5

The product of roots with the same index is equal to the root of the product

41611 \times 5

Calculate the product

208055

\frac{208055}{2 5 \times 5}

Multiply the numbers

More Steps

Evaluate

25 \times 5

When a square root of an expression is multiplied by itself,the result is that expression

2 \times 5

Multiply the terms

10

\frac{208055}{10}

h = \pm \frac{208055}{10}

Separate the equation into 2 possible cases

h = \frac{208055}{10} h = - \frac{208055}{10}

Solution

h_{1} = - \frac{208055}{10}, h_{2} = \frac{208055}{10}

Alternative Form

h_{1} \approx - 45.613046, h_{2} \approx 45.613046

Show Solution