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Question
a^{2}\times 850-1
Simplify the expression
850a^{2}-1
Evaluate
a^{2}\times 850-1
Solution
850a^{2}-1
Show Solutions
Find the roots
a_{1}=-\frac{\sqrt{34}}{170},a_{2}=\frac{\sqrt{34}}{170}
Alternative Form
a_{1}\approx -0.0343,a_{2}\approx 0.0343
Evaluate
a^{2}\times 850-1
To find the roots of the expression,set the expression equal to 0
a^{2}\times 850-1=0
Use the commutative property to reorder the terms
850a^{2}-1=0
Move the constant to the right-hand side and change its sign
850a^{2}=0+1
Removing 0 doesn't change the value,so remove it from the expression
850a^{2}=1
Divide both sides
\frac{850a^{2}}{850}=\frac{1}{850}
Divide the numbers
a^{2}=\frac{1}{850}
Take the root of both sides of the equation and remember to use both positive and negative roots
a=\pm \sqrt{\frac{1}{850}}
Simplify the expression
More Steps
Evaluate
\sqrt{\frac{1}{850}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt{1}}{\sqrt{850}}
Simplify the radical expression
\frac{1}{\sqrt{850}}
Simplify the radical expression
More Steps
Evaluate
\sqrt{850}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{25\times 34}
\text{Write the number in exponential form with the base of }5
\sqrt{5^{2}\times 34}
The root of a product is equal to the product of the roots of each factor
\sqrt{5^{2}}\times \sqrt{34}
\text{Reduce the index of the radical and exponent with }2
5\sqrt{34}
\frac{1}{5\sqrt{34}}
Multiply by the Conjugate
\frac{\sqrt{34}}{5\sqrt{34}\times \sqrt{34}}
Multiply the numbers
More Steps
Evaluate
5\sqrt{34}\times \sqrt{34}
When a square root of an expression is multiplied by itself,the result is that expression
5\times 34
Multiply the terms
170
\frac{\sqrt{34}}{170}
a=\pm \frac{\sqrt{34}}{170}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&a=\frac{\sqrt{34}}{170}\\&a=-\frac{\sqrt{34}}{170}\end{align}
Solution
a_{1}=-\frac{\sqrt{34}}{170},a_{2}=\frac{\sqrt{34}}{170}
Alternative Form
a_{1}\approx -0.0343,a_{2}\approx 0.0343
Show Solutions
