Solve h^2406-40-0

Question

Simplify the expression

406 h^{2} - 40

Evaluate

h^{2} \times 406 - 40 - 0

Use the commutative property to reorder the terms

406 h^{2} - 40 - 0

Solution

406 h^{2} - 40

Show Solution

2 (203 h^{2} - 20)

Evaluate

h^{2} \times 406 - 40 - 0

Use the commutative property to reorder the terms

406 h^{2} - 40 - 0

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

406 h^{2} - 40

Solution

2 (203 h^{2} - 20)

Show Solution

h_{1} = - \frac{2 1015}{203}, h_{2} = \frac{2 1015}{203}

Alternative Form

h_{1} \approx - 0.313882, h_{2} \approx 0.313882

Evaluate

h^{2} \times 406 - 40 - 0

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

h^{2} \times 406 - 40 - 0 = 0

Use the commutative property to reorder the terms

406 h^{2} - 40 - 0 = 0

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

406 h^{2} - 40 = 0

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

406 h^{2} = 0 + 40

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

406 h^{2} = 40

Divide both sides

\frac{406 h ^{2}}{406} = \frac{40}{406}

Divide the numbers

h^{2} = \frac{40}{406}

Cancel out the common factor 2

h^{2} = \frac{20}{203}

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

h = \pm \frac{20}{203}

Simplify the expression

More Steps

Evaluate

\frac{20}{203}

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

\frac{20}{203}

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{2 5}{203}

Multiply by the Conjugate

\frac{2 5 \times 203}{203 \times 203}

Multiply the numbers

More Steps

Evaluate

5 \times 203

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

5 \times 203

Calculate the product

1015

\frac{2 1015}{203 \times 203}

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

\frac{2 1015}{203}

h = \pm \frac{2 1015}{203}

Separate the equation into 2 possible cases

h = \frac{2 1015}{203} h = - \frac{2 1015}{203}

Solution

h_{1} = - \frac{2 1015}{203}, h_{2} = \frac{2 1015}{203}

Alternative Form

h_{1} \approx - 0.313882, h_{2} \approx 0.313882

Show Solution