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Question
11x\times 12.25118x\times 16.52-12
Simplify the expression
2226.2844296x^{2}-12
Evaluate
11x\times 12.25118x\times 16.52-12
Solution
More Steps
Evaluate
11x\times 12.25118x\times 16.52
Multiply the terms
More Steps
Evaluate
11\times 12.25118\times 16.52
Multiply the terms
134.76298\times 16.52
Multiply the numbers
2226.2844296
2226.2844296x\times x
Multiply the terms
2226.2844296x^{2}
2226.2844296x^{2}-12
Show Solutions
Factor the expression
\frac{1}{1250000}\left(2782855537x^{2}-15000000\right)
Evaluate
11x\times 12.25118x\times 16.52-12
Multiply
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Evaluate
11x\times 12.25118x\times 16.52
Multiply the terms
More Steps
Evaluate
11\times 12.25118\times 16.52
Multiply the terms
134.76298\times 16.52
Multiply the numbers
2226.2844296
2226.2844296x\times x
Multiply the terms
2226.2844296x^{2}
2226.2844296x^{2}-12
Convert the decimal into a fraction
More Steps
Evaluate
2226.2844296
Convert the decimal into a fraction
\frac{22262844296}{10000000}
Reduce the fraction
\frac{2782855537}{1250000}
\frac{2782855537}{1250000}x^{2}-12
Solution
\frac{1}{1250000}\left(2782855537x^{2}-15000000\right)
Show Solutions
Find the roots
x_{1}=-\frac{1000\sqrt{41742833055}}{2782855537},x_{2}=\frac{1000\sqrt{41742833055}}{2782855537}
Alternative Form
x_{1}\approx -0.073418,x_{2}\approx 0.073418
Evaluate
11x\times 12.25118x\times 16.52-12
To find the roots of the expression,set the expression equal to 0
11x\times 12.25118x\times 16.52-12=0
Multiply
More Steps
Multiply the terms
11x\times 12.25118x\times 16.52
Multiply the terms
More Steps
Evaluate
11\times 12.25118\times 16.52
Multiply the terms
134.76298\times 16.52
Multiply the numbers
2226.2844296
2226.2844296x\times x
Multiply the terms
2226.2844296x^{2}
2226.2844296x^{2}-12=0
Move the constant to the right-hand side and change its sign
2226.2844296x^{2}=0+12
Removing 0 doesn't change the value,so remove it from the expression
2226.2844296x^{2}=12
Divide both sides
\frac{2226.2844296x^{2}}{2226.2844296}=\frac{12}{2226.2844296}
Divide the numbers
x^{2}=\frac{12}{2226.2844296}
Divide the numbers
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Evaluate
\frac{12}{2226.2844296}
Convert the decimal into a fraction
More Steps
Evaluate
2226.2844296
Convert the decimal into a fraction
\frac{22262844296}{10000000}
Reduce the fraction
\frac{2782855537}{1250000}
\frac{12}{\frac{2782855537}{1250000}}
Multiply by the reciprocal
12\times \frac{1250000}{2782855537}
Multiply the numbers
\frac{12\times 1250000}{2782855537}
Multiply the numbers
\frac{15000000}{2782855537}
x^{2}=\frac{15000000}{2782855537}
Take the root of both sides of the equation and remember to use both positive and negative roots
x=\pm \sqrt{\frac{15000000}{2782855537}}
Simplify the expression
More Steps
Evaluate
\sqrt{\frac{15000000}{2782855537}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt{15000000}}{\sqrt{2782855537}}
Simplify the radical expression
More Steps
Evaluate
\sqrt{15000000}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{1000000\times 15}
\text{Write the number in exponential form with the base of }1000
\sqrt{1000^{2}\times 15}
The root of a product is equal to the product of the roots of each factor
\sqrt{1000^{2}}\times \sqrt{15}
\text{Reduce the index of the radical and exponent with }2
1000\sqrt{15}
\frac{1000\sqrt{15}}{\sqrt{2782855537}}
Multiply by the Conjugate
\frac{1000\sqrt{15}\times \sqrt{2782855537}}{\sqrt{2782855537}\times \sqrt{2782855537}}
Multiply the numbers
More Steps
Evaluate
\sqrt{15}\times \sqrt{2782855537}
The product of roots with the same index is equal to the root of the product
\sqrt{15\times 2782855537}
Calculate the product
\sqrt{41742833055}
\frac{1000\sqrt{41742833055}}{\sqrt{2782855537}\times \sqrt{2782855537}}
When a square root of an expression is multiplied by itself,the result is that expression
\frac{1000\sqrt{41742833055}}{2782855537}
x=\pm \frac{1000\sqrt{41742833055}}{2782855537}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{1000\sqrt{41742833055}}{2782855537}\\&x=-\frac{1000\sqrt{41742833055}}{2782855537}\end{align}
Solution
x_{1}=-\frac{1000\sqrt{41742833055}}{2782855537},x_{2}=\frac{1000\sqrt{41742833055}}{2782855537}
Alternative Form
x_{1}\approx -0.073418,x_{2}\approx 0.073418
Show Solutions
