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Question
h^{2}\times 10-1\frac{3}{4}
Simplify the expression
10h^{2}-\frac{7}{4}
Evaluate
h^{2}\times 10-1\frac{3}{4}
Covert the mixed number to an improper fraction
More Steps
Convert the expressions
1\frac{3}{4}
Multiply the denominator of the fraction by the whole number and add the numerator of the fraction
\frac{4+3}{4}
Add the terms
\frac{7}{4}
h^{2}\times 10-\frac{7}{4}
Solution
10h^{2}-\frac{7}{4}
Show Solutions
Factor the expression
\frac{1}{4}\left(40h^{2}-7\right)
Evaluate
h^{2}\times 10-1\frac{3}{4}
Covert the mixed number to an improper fraction
More Steps
Convert the expressions
1\frac{3}{4}
Multiply the denominator of the fraction by the whole number and add the numerator of the fraction
\frac{4+3}{4}
Add the terms
\frac{7}{4}
h^{2}\times 10-\frac{7}{4}
Use the commutative property to reorder the terms
10h^{2}-\frac{7}{4}
Solution
\frac{1}{4}\left(40h^{2}-7\right)
Show Solutions
Find the roots
h_{1}=-\frac{\sqrt{70}}{20},h_{2}=\frac{\sqrt{70}}{20}
Alternative Form
h_{1}\approx -0.41833,h_{2}\approx 0.41833
Evaluate
h^{2}\times 10-1\frac{3}{4}
To find the roots of the expression,set the expression equal to 0
h^{2}\times 10-1\frac{3}{4}=0
Covert the mixed number to an improper fraction
More Steps
Convert the expressions
1\frac{3}{4}
Multiply the denominator of the fraction by the whole number and add the numerator of the fraction
\frac{4+3}{4}
Add the terms
\frac{7}{4}
h^{2}\times 10-\frac{7}{4}=0
Use the commutative property to reorder the terms
10h^{2}-\frac{7}{4}=0
Move the constant to the right-hand side and change its sign
10h^{2}=0+\frac{7}{4}
Add the terms
10h^{2}=\frac{7}{4}
Multiply by the reciprocal
10h^{2}\times \frac{1}{10}=\frac{7}{4}\times \frac{1}{10}
Multiply
h^{2}=\frac{7}{4}\times \frac{1}{10}
Multiply
More Steps
Evaluate
\frac{7}{4}\times \frac{1}{10}
To multiply the fractions,multiply the numerators and denominators separately
\frac{7}{4\times 10}
Multiply the numbers
\frac{7}{40}
h^{2}=\frac{7}{40}
Take the root of both sides of the equation and remember to use both positive and negative roots
h=\pm \sqrt{\frac{7}{40}}
Simplify the expression
More Steps
Evaluate
\sqrt{\frac{7}{40}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt{7}}{\sqrt{40}}
Simplify the radical expression
More Steps
Evaluate
\sqrt{40}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{4\times 10}
\text{Write the number in exponential form with the base of }2
\sqrt{2^{2}\times 10}
The root of a product is equal to the product of the roots of each factor
\sqrt{2^{2}}\times \sqrt{10}
\text{Reduce the index of the radical and exponent with }2
2\sqrt{10}
\frac{\sqrt{7}}{2\sqrt{10}}
Multiply by the Conjugate
\frac{\sqrt{7}\times \sqrt{10}}{2\sqrt{10}\times \sqrt{10}}
Multiply the numbers
More Steps
Evaluate
\sqrt{7}\times \sqrt{10}
The product of roots with the same index is equal to the root of the product
\sqrt{7\times 10}
Calculate the product
\sqrt{70}
\frac{\sqrt{70}}{2\sqrt{10}\times \sqrt{10}}
Multiply the numbers
More Steps
Evaluate
2\sqrt{10}\times \sqrt{10}
When a square root of an expression is multiplied by itself,the result is that expression
2\times 10
Multiply the terms
20
\frac{\sqrt{70}}{20}
h=\pm \frac{\sqrt{70}}{20}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&h=\frac{\sqrt{70}}{20}\\&h=-\frac{\sqrt{70}}{20}\end{align}
Solution
h_{1}=-\frac{\sqrt{70}}{20},h_{2}=\frac{\sqrt{70}}{20}
Alternative Form
h_{1}\approx -0.41833,h_{2}\approx 0.41833
Show Solutions
