Solve h^2406-112-0

Question

Simplify the expression

406 h^{2} - 112

Evaluate

h^{2} \times 406 - 112 - 0

Use the commutative property to reorder the terms

406 h^{2} - 112 - 0

Solution

406 h^{2} - 112

Show Solution

14 (29 h^{2} - 8)

Evaluate

h^{2} \times 406 - 112 - 0

Use the commutative property to reorder the terms

406 h^{2} - 112 - 0

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

406 h^{2} - 112

Solution

14 (29 h^{2} - 8)

Show Solution

h_{1} = - \frac{2 58}{29}, h_{2} = \frac{2 58}{29}

Alternative Form

h_{1} \approx - 0.525226, h_{2} \approx 0.525226

Evaluate

h^{2} \times 406 - 112 - 0

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

h^{2} \times 406 - 112 - 0 = 0

Use the commutative property to reorder the terms

406 h^{2} - 112 - 0 = 0

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

406 h^{2} - 112 = 0

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

406 h^{2} = 0 + 112

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

406 h^{2} = 112

Divide both sides

\frac{406 h ^{2}}{406} = \frac{112}{406}

Divide the numbers

h^{2} = \frac{112}{406}

Cancel out the common factor 14

h^{2} = \frac{8}{29}

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

h = \pm \frac{8}{29}

Simplify the expression

More Steps

Evaluate

\frac{8}{29}

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

\frac{8}{29}

Simplify the radical expression

More Steps

Evaluate

8

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

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

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

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{2 2}{29}

Multiply by the Conjugate

\frac{2 2 \times 29}{29 \times 29}

Multiply the numbers

More Steps

Evaluate

2 \times 29

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

2 \times 29

Calculate the product

58

\frac{2 58}{29 \times 29}

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

\frac{2 58}{29}

h = \pm \frac{2 58}{29}

Separate the equation into 2 possible cases

h = \frac{2 58}{29} h = - \frac{2 58}{29}

Solution

h_{1} = - \frac{2 58}{29}, h_{2} = \frac{2 58}{29}

Alternative Form

h_{1} \approx - 0.525226, h_{2} \approx 0.525226

Show Solution