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Question
9x^{2}\times 6-39
Simplify the expression
54x^{2}-39
Evaluate
9x^{2}\times 6-39
Solution
54x^{2}-39
Show Solutions
Factor the expression
3\left(18x^{2}-13\right)
Evaluate
9x^{2}\times 6-39
Multiply the terms
54x^{2}-39
Solution
3\left(18x^{2}-13\right)
Show Solutions
Find the roots
x_{1}=-\frac{\sqrt{26}}{6},x_{2}=\frac{\sqrt{26}}{6}
Alternative Form
x_{1}\approx -0.849837,x_{2}\approx 0.849837
Evaluate
9x^{2}\times 6-39
To find the roots of the expression,set the expression equal to 0
9x^{2}\times 6-39=0
Multiply the terms
54x^{2}-39=0
Move the constant to the right-hand side and change its sign
54x^{2}=0+39
Removing 0 doesn't change the value,so remove it from the expression
54x^{2}=39
Divide both sides
\frac{54x^{2}}{54}=\frac{39}{54}
Divide the numbers
x^{2}=\frac{39}{54}
\text{Cancel out the common factor }3
x^{2}=\frac{13}{18}
Take the root of both sides of the equation and remember to use both positive and negative roots
x=\pm \sqrt{\frac{13}{18}}
Simplify the expression
More Steps
Evaluate
\sqrt{\frac{13}{18}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt{13}}{\sqrt{18}}
Simplify the radical expression
More Steps
Evaluate
\sqrt{18}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{9\times 2}
\text{Write the number in exponential form with the base of }3
\sqrt{3^{2}\times 2}
The root of a product is equal to the product of the roots of each factor
\sqrt{3^{2}}\times \sqrt{2}
\text{Reduce the index of the radical and exponent with }2
3\sqrt{2}
\frac{\sqrt{13}}{3\sqrt{2}}
Multiply by the Conjugate
\frac{\sqrt{13}\times \sqrt{2}}{3\sqrt{2}\times \sqrt{2}}
Multiply the numbers
More Steps
Evaluate
\sqrt{13}\times \sqrt{2}
The product of roots with the same index is equal to the root of the product
\sqrt{13\times 2}
Calculate the product
\sqrt{26}
\frac{\sqrt{26}}{3\sqrt{2}\times \sqrt{2}}
Multiply the numbers
More Steps
Evaluate
3\sqrt{2}\times \sqrt{2}
When a square root of an expression is multiplied by itself,the result is that expression
3\times 2
Multiply the terms
6
\frac{\sqrt{26}}{6}
x=\pm \frac{\sqrt{26}}{6}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{\sqrt{26}}{6}\\&x=-\frac{\sqrt{26}}{6}\end{align}
Solution
x_{1}=-\frac{\sqrt{26}}{6},x_{2}=\frac{\sqrt{26}}{6}
Alternative Form
x_{1}\approx -0.849837,x_{2}\approx 0.849837
Show Solutions
